theory group at dep. phys. “enrico fermi” · luc, lui, giam francesco (b): daniele ... an...

Congressino Dip Fis 11/4/2011

• “Theories of the fundamental interactions towards 2020” D. Anselmi, A. Strumia, L. Bracci, G. Cicogna, F. Bigazzi, E. Meggiolaro, G. Paffuti, C. Giannessi, S. Servadio, P. Christillen, K. Konishi; A. Di Giacomo, L. Picasso, T. Elze, G. Morchio, E. D’Emilio, T. Fujimori, Y. Jiang, M. Cipriani, A. Michelini, D. Dorigoni, S. Giacomelli, M. Taiuti, E. Ciuffoli, C. Bonati, R. Torre, P. Giardino,

• “A survey of quantum field theory and applications” E. Vicari, P. Rossi, E. Guadagnini, M. Campostrini, M.Mintchev, B. Alles, P. Calabrese; P. Menotti, C. Torrero, G. Paoletti, G. Ceccarelli, E. Profumo, M. Fagotti

• “Theoretical nuclear physics” I. Bombaci, A. Bonaccorso, M. Viviani, A. Kievsky, L. Marcucci; S. Rosati, R. Kumar

The Speakers

Theory Group at Dep. Phys. “Enrico Fermi”

Tuesday, April 12, 2011

Fundamental Problems in Physics TodayThree “melodies” of the 20th C Theoretical Physics: (C.N. Yang 2002)

“Quantization, Symmetries and Phase Factors”

• Quantum gravity?

◦ String theory? • New principles? New paradigm? Holographic principle?

Black-hole entropy?

• Cosmology

• Quark Confinement (non-Abelian strong gauge dynamics) ?

• Quantum mechanics : fundamental aspects. Time? Schrödinger’s cat

• Higgs? Supersymmetry ? GUTS?

BUT !!Origin of mass?

Observational Cosmology and Astroparticle physics

COBE, WMAP, SDSS, ... FERMI/LAT , AMS...

Origin of the universe?

dark matter? dark energy? GRB, UHECR

ν ?

Local, renormalizable gauge theory (of pointlike objects - the elementary particles)

AdS/CFT?

Entanglement/Quantum computing

Why MW / MPlanck ~ 10-17

“naturalness/hierarchy” problem

“Standard Model” of the fundamental interactionsSU(3)QCD x (SU(2)xU(1))GWS ’70-’74➩

mν ≪ me , mu ≪ mc ≪ mt ?

Ωm =0.26±0.02; ΩΛ =0.74±0.02; Ωb =0.04;

◦ Lorentz Invariance Violation at short distances?

LHC

η problem?

σtot ∿ log2 s ? Quark-gluon plasma, Color superconductivity?

μ problem?

StandardCosmology

Anomaly cancellations !

◦ Susy breaking? Extra dimensions?

We are perhaps at the pre-dawn of a new scientific revolution

Pn = |!n|!"|2 ?

Glashow-Weinberg-Salam’s Electroweak theory

Maldacena ’97

Quant. chromodynamicsNuclear forces

BIG BANG / Inflation


This presentation

Alessandro

DamianoEnrico

Ken & Com.

Adriano and Com.

Thomas

Luc, Lui, Giam

Francesco (B):

Daniele

Giampiero & Ken

END

Gianni


☞


arXiv:1012.4515 and 1009.0224

We found that electroweak corrections are relevant if DM is heavier than theweak scale, and included them in a public code.

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We provide ingredients and recipes for computing signals of TeV-scale

Dark Matter annihilations and decays in the Galaxy and beyond.

⏎Tuesday, April 12, 2011

Idea: use the violation of Lorentz symmetry

that are normally nonrenormalizable

Higher powers of momenta in dispersion relations and propagators make the

integrands of Feynman diagrams

A modified power counting criterion, which assigns different weights to space and

time, controls the UV behavior and the

Apart from violating Lorentz symmetry, the theory remains

polynomial, unitary and causal (with causality defined according to

Bogoliubov, which only needs past and future, no light cones

No counterterms with higher time derivatives

(perturbative) unitarity is safe

Since the purpose is to cure the UV behavior

interactions, Lorentz symmetry can be recovered in the IR by a fine tuning

of parameters. It is possible to have agreement with data

Lorentz violating renormalizableDamiano

+ Emilio Ciuffoli, Martina Taiuti and now Dario

symmetry to renormalize interactions

nonrenormalizable

in dispersion relations and propagators make the

integrands of Feynman diagrams more convergent in the UV

A modified power counting criterion, which assigns different weights to space and

and the renormalizability of the theory

Apart from violating Lorentz symmetry, the theory remains renormalizable, local,

with causality defined according to

, which only needs past and future, no light cones)

higher time derivatives are generated by renormalization, so

behavior of otherwise nonrenormalizable

interactions, Lorentz symmetry can be recovered in the IR by a fine tuning

of parameters. It is possible to have agreement with data

renormalizable Standard ModelDamiano Anselmi

and now Dario Buttazzo and Diego Redigolo


Consider the free theory (a hat denotes time

Its propagator is

and the dispersion relation reads

The improved ultraviolet behavior allows us to renormalize otherwise non

renormalizable vertices. They can be classified using a

time, a bar denotes space)

allows us to renormalize otherwise non-

vertices. They can be classified using a weighted power counting


Both vertices are compatible with a scale of

which agrees with present data (possibly apartenergy cosmic rays), if Lorentz symmetry isbroken at much larger energies)

An example of nonrenormalizable vertex that

which gives neutrinos Majorana masses after

Other examples are the four-fermion vertices

at the fundamental level.

Four-fermion vertices are bounded by existing

Lorentz violation

apart from the still mysterious ultrahigh-violated but CPT is preserved (or

that becomes renormalizable is

after symmetry breaking.

vertices

existing limits on proton decay.

(10-28 - 10-29 cm )


The model contains four fermion interactions

describe the known low-energy physics in the

masses to fermions and gauge bosons dynamically. The

field and arises as a low-energy effect

We can build a Standard Model extension without elementary scalars

An interesting low-energy prediction is the formula

which is in perfect agreement with data for

where

interactions at the fundamental level. It is possible to

energy physics in the Nambu—Jona-Lasinio spirit, which gives

dynamically. The Higgs field is a composite

We can build a Standard Model extension without elementary scalars

energy prediction is the formula


Formulation of Lorentz Violating Stardard

D.A., Weighted power counting, neutrino massesthe Standard Model, Phys. Rev. D 79 (2009) 025017 and

Scalarless LVSM and its phenomenology:I build a version with no fundamental scalar and

D.A., Standard Model Without Elementary Scalars And High Energy Lorentz ViolationPhys. J. C 65 (2010) 523 and arXiv:0904.1849 [

Detailed analysis of low-energy phenomenology of We show that we can find agreement with all data, within theoretical errors

D.A. and E. Ciuffoli, Low-energy phenomenology of with high-energy Lorentz violation, Phys. Rev. D 83 (2011) 056005 andarXiv:1101.2014 [hep-ph]

Experimental limits and theoretical analysis on the scale of Lorentz Here we show that is consistent with all data (at preserved CPT).

We claim that in Nature Lorentz symmetry may be broken well below the Planck scale

D.A. and M. Taiuti, Vacuum Cherenkov radiation in quantum electrodynamics with energy Lorentz violation, PRD in print and arXiv:1101.2019 [

Summary of research topics and recent papers

Stardard Model (LVSM):

masses and Lorentz violating extensions of. Rev. D 79 (2009) 025017 and arXiv:0808.3475 [hep-ph]

phenomenology:scalar and analyse its phenomenology

Standard Model Without Elementary Scalars And High Energy Lorentz Violation, Eur. arXiv:0904.1849 [hep-ph]

phenomenology of scalarless LVSM:We show that we can find agreement with all data, within theoretical errors

energy phenomenology of scalarless Standard Model extensions Phys. Rev. D 83 (2011) 056005 and

limits and theoretical analysis on the scale of Lorentz violation:Here we show that is consistent with all data (at preserved CPT).

We claim that in Nature Lorentz symmetry may be broken well below the Planck scale

Vacuum Cherenkov radiation in quantum electrodynamics with high-PRD in print and arXiv:1101.2019 [hep-ph]

papers


Attivita di ricerca di ENRICO MEGGIOLARO

Di!usione “so!ce” ad alta energia in QCD


Usando un approccio basato sull’integrale funzionale, le ampiezzedi di!usione elastica adrone–adrone (e.g., mesone–mesone), adalta energia (

!s " 1 GeV) e “so!ci” (

!|t| ! 1 GeV), vengono

ricostruite da certe funzioni di correlazione di due “loop di Wilson”nello spazio–tempo di Minkowski (ampiezze dipolo–dipolo).




In [M. Giordano, E. Meggiolaro, Phys. Rev. D 78 (2008) 074510;Phys. Rev. D 81 (2010) 074022] il problema e stato a!rontato(per la prima volta) dal punto di vista della QCD su reticolo,mediante un calcolo diretto (utilizzando l’infrastruttura GRIDdell’I.N.F.N.), con simulazioni Monte Carlo nella teoria di puragauge SU(3), della funzione di correlazione Euclidea di dueloop di Wilson, da cui l’ampiezza di di!usione mesone–mesone puoessere ricostruita mediante continuazione analitica.[M. Giordano, E. Meggiolaro, Phys. Lett. B 675 (2009) 123-132;M. Giordano, Tesi di Dottorato, Pisa, 20/10/2009; relatore: E. M.]

Questo e attualmente l’UNICO approccio al problema delladi!usione “so"ce” adrone–adrone ad alta energia da principi primi(QCD) e non–perturbativo.=! I modelli analitici testati (SVM, ILM, AdS/CFT) risultanoinsoddisfacenti. Si cercano nuove forme funzionali che fittinomeglio i dati su reticolo . . .

------------------

------------------------------------------




[E. Meggiolaro, M. Giordano, “High–energy hadron–hadron(dipole–dipole) scattering on the lattice”; E–print: arXiv:1010.0914[hep–lat]; presentato da E. Meggiolaro al simposio della conferenzaHESI 2010, 10–13 agosto 2010, Kyoto, Giappone.]

. . . La speranza e quella di riuscire a spiegare il comportamento(universale?) ad alta energia delle sezioni d’urto adrone–adronea partire dall’ampiezza (fondamentale) dipolo–dipolo, calcolatanell’Euclideo: alcuni risultati preliminari sembrano condurre a!tot(s) ! (ln s)2, in accordo coi dati sperimentali (e con illimite di Froissart) . . . [Work in progress]



Simmetrie chirali e topologia in QCD (anche per T > 0)

Simmetrie chirali e topologia in QCD (anche per T > 0)

Si studia un modello di Lagrangiana Chirale E!cace che include(oltre all’usuale condensato chirale !qq" e all’anomalia) anche uncerto condensato U(1) assiale (irriducibile) del tipo:

CU(1) # ![detst

(qsRqtL) + detst

(qsLqtR)]",

che agisce come parametro d’ordine per la sola simmetria U(1)assiale e resta diverso da zero attraverso la transizione chirale aTch $ 170 MeV, fino a una certa temperatura TU(1) > Tch.=% implicazioni fenomenologiche, per esempio (per T < Tch):i) nei decadimenti radiativi !, !! & ""[M. Marchi, E. Meggiolaro, Nucl. Phys. B 665 (2003) 425;E. Meggiolaro, Phys. Rev. D 69 (2004) 074017.]ii) nei decadimenti forti !, !! & 3#, !! & !##[E. Meggiolaro, E–print: arXiv:1010.1140 [hep–ph]; Phys. Rev. D(2011), in stampa.] ⏎


Confinement in QCDnonperturbative methods on and o! the lattice

PeoplePisa: C. Bonati, A. Di GiacomoActive collaboration: M. D’Elia, P. Incardona (Genova),F. Sanfilippo (Roma), G. Cossu (KEK, Japan)Starting collaboration: APE group (Roma), M. Caselle (Torino)

Main interests and recent works:Mechanism of color confinementvacuum dual superconductivitythrough monopole condensation

Nucl. Phys. B 828, 390 (2010),Phys. Rev. D 81, 085022 (2010),Phys. Rev. D 82, 094509 (2010),

QCD phase diagramcritical points & universalityclasses

JHEP 0907, 048 (2009),Phys. Rev. D. 82 114515 (2010),arXiv:1011.4515 [hep-lat](accepted in PRD)

☜


Dual superconductivity & monopoles

ContinuumThe gauge independence ofthe monopole definition wasestablished.

Lattice

! The gauge dependence of themonopole detection wasclarified.

! A revised version of themonopole operator wasintroduced.

-6 -4 -2 0 2 4 6 8 10

(!-!c)N

s

1/"

-0.04

-0.03

-0.02

-0.01

0

0.01

(#~-#~

b)/

Ns1

/"

Ns=16

Ns=20

Ns=24

SU(2) gauge theory 4xNs

3

Wu-Yang monopole of chage 4

1. The problems of the previousimplementation are solved.

2. Good scaling at deconfinementtransition.

Perspectives: the revised order parameter can now beused to investigate confinement in real QCD and inother confining theories (e.g. G2 gauge theory)


QCD phase diagram

T

1st

1st

crossoverZ2

Z2

O(4)

0

!

ms

mu !

Nf = 2 chiral transition

Study of the structure of the QCD phasediagram at finite temperature and density,with particular emphasis on those aspectsof the phase diagram related to knownsymmetries of QCD (i.e. chiral symmetry)

Main focus: determination of the order Nf = 2 chiral transition.Previous studies of the group, Phys. Rev. D 72, 114510 (2005),indicated the first order nature of the transition, which is usually

believed to be 2nd order.Huge computational resources needed!


Computational toolsThe video game market developments compelled graphic cards

manufacturers to increase the floating point calculationperformance of their products ! New architecture for

computations: Graphic Processing Units (GPUs)

Need to rewrite all codes and some care is needed in optimizations(see arXiv:1010.5433) but TOTALLY WORTH IT!

With our current implementation1 GPU "! 1# 3 apeNEXT crates

possible present alternatives (e.g. CPU clusters) lose afactor 3 in price and 6 in power consumption

Ongoing developments:

! (short-term) parallelize the work between several GPUs(in collaboration with the APE group)

! (long-term) fermions with improved chiral properties(still more computationally demanding!) ⏎


---------------------------


L. Bracci e L. E. Picasso: rappresentazioni algebra diWeyl

In Rn : U(!) ! e"i!

!ipi V (") ! e"i!

"iqi, U(!)V (") = ei!·"V (")U(!)von Neumann: RI equivalenti; rappres. completamente riducibili.

Spazio semilimitato U(!) semigruppo isometrie, V (") gruppo##(q) = [x0,$), R I con dato x0 equivalenti1. Z ! Centro = {$I} #H = %iHi, Hi irriducibili, stesso x0. #(q) e omogeneo in [x0,$) 4.In generale: integrale di Hi con diversi x0

4.Irriducibilita & irrid. rispetto agli U(!) 1. L’algebra per R, per spaziosemilimitato e quella generata da {U(!)} sono identiche 5.

Segmento U(!) isometrie parziali, U(0) = I, U(1) = 0##(q) = [x0, x0 + 1], RI con lo stesso x0 equivalenti 1,3.

Z = {!I}! rappresentazioni completamente riducibili 3.Se !U("), !V (n) unitari che obbediscono Weyl, per RI e !U(1) = ei#I.RI con dato # sono equivalenti. Se !U(1) = ei#I e Z = {!I} 3.

Sfera Algebra A generata da $n e $J e E3 (gruppo euclideo 3-dim.)Le RI sono le RI (l0,0) di so(3,1). Casimir $J · $n " % = ±l0. A esottoalgebra di AS generata da $n, $L, $S, ! per particella di spin S, Hirriducibile sotto AS, e H = #%=S

%=$SH%, H% sede della RI (|%|,0) di Acon $J · $n = % 6.

Spazio non semplicemente connesso RI non equivalenti. Nel pianobucato, {$q,$i%} e {$q,$i% + $f($r)}, % & $f = 0, non equivalenti se"&

$f($r) · d$r '= 0 ! re-interpretazione e!etto Aharonov-Bohm: H =

Hlibera = $p2

2m, ma






Hlibera = $p2

2m, ma







Hlibera = $p2

2m, ma

!p = !i"+ !f(!r), !f = !2"!r2

(!x2, x1),!#

!fd!r = ! .

! #= 2n" $ e"etto Aharonov-Bohm. Quindi A-B segue dall’esistenzadi RI non equivalenti. E l’osservazione che determina quale ! (qualerappresentazione) scegliere 2.

1) Journal Math. Phys. 47 112102 (2006)2) American J. Phys. 75 268 (2007)3) Bull. London Math. Soc. 39 791 (2007)4) Lett. Math. Phys. 89 277 (2009)5) Lett. Math. Phys. 93 267 (2010)6) Eur. Phys. J. Plus 126 4 (2011l

G. Cicogna:Studio analitico e algebrico di equazioni differenziali non lineari di interesse fisico. Speciale attenzione e' dedicata alla introduzione di opportune generalizzazioni della nozione di algebra di Lie delle simmetrie. Le applicazioni includono: problemi nella fisica dei plasmi, fenomeni di biforcazione, comparsa di soluzioni periodiche e/o complesse, tecniche di riduzione e di integrazione, leggi di conservazione generalizzate. ⏎


1. Algebre di Poisson non commutative, invarianza per diffeomorfismi e quantizzazione

Risultati: A) MQ sulle varietà differenziabili B) Derivazione della quantizzazione di Dirac senza inconsistenze

2. Estensione delle previsioni della MQ e dise-

guaglianze di Boole-Bell

3. La matrice di scattering in QED: esistenza,

costruzione non perturbativa. Possibile costruzione dei campi carichi asintoti-

ci attraverso correzioni di stringa che superano lʼostruzione data dallʼassenza di stati carichi a massa definita.

4. Risultati esatti su identità di Ward, topologia e simmetria chirale in QCD:

More about it


Progetti:

- Gradi di libertà interni e diffeomorfismi

- Covarianza e invarianza per diffeomorfisimi in gravità quantistica

- Possibilità di una descrizione completa di matrice S in QED via LSZ modificato

- Implicazioni dei modelli e della costruzione LSZ generalizzata sulla localizzabilità e la classificazione degli stati carichi in QED

- Implicazioni della struttura delle osservabili locali sulle identità di Ward del problema U(1) e sul problema CP forte

- Parametri e gerarchie di massa in supercon-

duttività oltre il BCS

⏎


!"#$%&'()*

!"#$%&'"()*+,%&-)#.,/$&0#1*"#2&34/,$&56/)(4/'&7%&2/1*'&)8&&6),)+(1.64-&$#1,'9&

4:/:&;/1<,%&-)#.,/$&&64+6/(&$42/*'4)*1,&&"6/)(4/'&)8&+(1=4"%&>'"(4*+'?&:&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

!'+#,"+#'$*

!"()*+,%&-)#.,/$&035'&1(4'/&4*&21*%&.,1-/':&@A12.,/'B

C 0DE&>-)*84*/2/*"9&21''&+1.9&F#1(<C!"#$%&'"()*(&'+(),&(-&./01&(%2&3/145

C F#1*"#2&-(4"4-1,&.)4*"'&4*&-)*$/*'/$&21""/(

C #,"(1-),$ 3/(24&+1'/'&1"&#*4"1(4"%

C >./(61.'?&'#./(-)*$#-")('&;4"6&64+6&-(4"4-1,&"/2./(1"#(/&

C "6/)(/"4-1,&'-/*1(4)'&7/%)*$&"6/&!"1*$1($&G)$/,&)8&.1("4-,/&.6%'4-':

! H//$&")&$/=/,).&*)*C./("#(71"4=/&")),':

! I),)+(1.6% 4'&/2/(+4*+&1'&1&.()24'4*+&)*/:&

! J8"/*&1,,);'&1*1,%"4-&-)*"(),&)*&"6/&2)$/,':&&K()=4$/'&*)=/,&4*"#4"4)*:

! L,,);'&")&$/1,&7)"6&;4"6&'"1"4-&1*$&(/1,C"42/&$%*124-1,&.()./("4/':&

! L&,)"&)8&;)(<&'"4,,&*//$/$&")&1..,%&4"&")&.6/*)2/*),)+4-1,&2)$/,':

3(1*-/'-)&M4+1NN4 >OH3H?


• Nonabelian vortices: (non-Abelian monopoles and confinement )

K. Konishi and Fujimori, Jiang, Dorigoni,

Michelini, Giacomelli, Cipriani

+ Carlino, Murayama, Spanu, Grena, Auzzi, Yung, Bolognesi,Ferretti, Nitta, Ookouchi, Ohashi, Yokoi, Marmorini, Vinci, Eto, Gudnason, Evslin

(Armenia-Italy-Japan-USA-Russia-Denmark-China Collaboration)

• Faddeev-Niemi decomposition for Yang-Mills theories

• Large N, dimensionally reduced SU(N) SYM

Evslin, Giacomelli+

Michelini, Konishi

Dorigoni, Veneziano,Wosiek

’03-’11

’10-’11

’10

• “Almost conformal” vacua for confinement Auzzi, Grena, Konishi, ’03 Giacomelli


• Dirac’s quantization condition ( ’31 -- But he no longer believed it ’80)

Nonabelian vortex, monopole and quark confinement

• ’t Hooft-Polyakov monopoles (’74)

• Vortex in Landau-Ginzburg theory (Abrikosov ’52, Nielsen, Olesen’74)

• Confinement by monopole condensation (dual Meissner effect) (Mandelstam, ‘t Hooft ’80)

But no evidence of dynamical abelianization

• Nonabelian monopoles? Quantum mechanical nonabelian monopoles do appear in N=2 susy theories (Carlino, Konishi, Murayama, 2000)

• Nonabelian vortices: discovered by the Pisa group in 2003

➪ Rich and deep physics results

e · g = n/2, n= ±1,±2,...

◦ Vortex effective world sheet action ➭ GNO duality

GUT? ➟ Inflation

◦ 4D gauge dynamics = 2D sigma model

◦ Vortices in high-density QCD; multicomponent superconductivity

’03-’11Pisa,

Minnesota,Cambridge,

Tokyo,... ...

Seiberg-Wittenexact solns N=2

’94

◦ Role of the Global symmetry in dual gauge group

◦ Fractional vortices

◦ Monopole-vortex complex soliton Attracting the interest ofmathematics communitiy


S.B. Gudnason, Y. Jiang, K. Konishi, "Non-Abelian vortex dynamics: Effective world-sheet action". JHEP 1008:012, 2010. (2010) e-Print: arXiv:1007.2116 [hep-th].

M. Eto, T. Fujimori, S.B. Gudnason, Y. Jiang, K. Konishi, M. Nitta, K. Ohashi, "Group Theory of Non-Abelian Vortices". JHEP 1011:042, (2010). e-Print: arXiv:1009.4794 [hep-th].

M. Eto, J. Evslin, K. Konishi, G. Marmorini, M. Nitta, K. Ohashi, W. Vinci, N. Yokoi (2007), "On the moduli space of semilocal strings and lumps", Phys. Rev. D76:105002, (2007), arXiv:0704.2218 [hep-th].

K. Konishi "The Magnetic Monopoles Seventy-Five Years Later", Lecture Notes in Physics, (vol. 1, pp. 473-532). (2007). ISBN-10: 3540742328: Springer.

M. Eto, K. Konishi, G. Marmorini, M. Nitta, K. Ohashi, W. Vinci, N. Yokoi, "Non-Abelian Vortices of Higher Winding Numbers", Phys. Rev. D, vol. D74, 065021, (2006).

K. Konishi, R. Auzzi, S. Bolognesi, J. Evslin, "NonAbelian monopoles and the vortices that confine them", Nucl. Phys. B686, 119 (2004).

K. Konishi, R. Auzzi, S. Bolognesi, A. Yung, J. Evslin, "Nonabelian superconductors: vortices and confinement in N=2 SQCD", Nucl. Phys. B673, 187 (2003). e-Print: hep-th/0307287.

G. Carlino, K. Konishi, H. Murayama, "Dynamical symmetry breaking in supersymmetric SU(n(c)) and USp(2n(c)) gauge theories", Nucl. Phys. B 608, 51 (2001) e-Print: hep-th/0005076.

Some References


Gauge profile function f !!,z"

0

5

10

15

20

!20

!10

0

10

20!2.0

!1.5

!1.0

Gauge profile function l!!,z"

0

10

20

30

40

!50

0

50

0.0

0.5

1.0

Scalar profile function s!!,z"

0

5

10

15

20!20

!10

0

10

20

0.0

0.5

1.0

Quark profile function q!!,z"

0

10

20

30

40

!50

0

50

0.0

0.5

1.0

Figure 3: The four complex profile functions

!30 !20 !10 0 10

!20

!10

0

10

20

Figure 4: The behaviour of the magnetic field in the complex

15

Gauge profile function f !!,z"

0

5

10

15

20

!20

!10

0

10

20!2.0

!1.5

!1.0

Gauge profile function l!!,z"

0

10

20

30

40

!50

0

50

0.0

0.5

1.0

Scalar profile function s!!,z"

0

5

10

15

20!20

!10

0

10

20

0.0

0.5

1.0

Quark profile function q!!,z"

0

10

20

30

40

!50

0

50

0.0

0.5

1.0

Figure 3: The four complex profile functions

!30 !20 !10 0 10

!20

!10

0

10

20

Figure 4: The behaviour of the magnetic field in the complex

15

⏎

Monopole-Vortex

complex

Cipriani, Gudnason, Dorigoni,

Fujimori, Konishi, Michelini ’11

Fig. 5: The energy (the left-most and the 2nd left panels) and the magnetic flux (the 2nd right panels) density,

together with the boundary values (A, B) (the right-most panel) for the minimal lump of the first type in the

strong gauge coupling limit. The moduli parameters are fixed as a1 = 0, a2 = 1, b1 = !1 in Eq. (4.18). The red

dots are zeros of A and the black one is the zero of B. ! = 1. The last figures illustrates the minimum lump

defined at exactly the orbifold point (see Eq. (4.20)) with Avev = 1/"

2, and with b = 0.8.14

“Fractional vortex” Eto et. al. ’09

Vortex orientational zeromodes


Dorigoni in collaboration with Veneziano, WosiekIDEA:

! Studying QCD-Like theories spectra in the Large-N limit,! Volume independence + Discretized Light-Cone quantization

! reduces computation to quantum mechanics problem.Model Studied: SYM4 reduced to N = (2, 2) in d = 2Observations:

! String-like spectrum Mn " T #!x$n,! Quantized distance between partons #!x$n.

|Wavefunctions|2 in coordinate space for two and three partons:

!100 !50 0 50 1000.0

0.2

0.4

0.6

0.8

1.0

!100 !50 0 50 1000.0

0.1

0.2

0.3

0.4

0.5

!100 !50 0 50 1000.0

0.1

0.2

0.3

0.4

0.5

!100 !50 0 50 1000.0

0.1

0.2

0.3

0.4

0.5

!100 !50 0 50 1000.0

0.1

0.2

0.3

0.4

0.5

!50 0 50 1000.0

0.1

0.2

0.3

0.4

0.5

Dorigoni in collaboration with Veneziano, WosiekIDEA:

! Studying QCD-Like theories spectra in the Large-N limit,! Volume independence + Discretized Light-Cone quantization

! reduces computation to quantum mechanics problem.Model Studied: SYM4 reduced to N = (2, 2) in d = 2Observations:

! String-like spectrum Mn " T #!x$n,! Quantized distance between partons #!x$n.

|Wavefunctions|2 in coordinate space for two and three partons:

!100 !50 0 50 1000.0

0.2

0.4

0.6

0.8

1.0

!100 !50 0 50 1000.0

0.1

0.2

0.3

0.4

0.5

!100 !50 0 50 1000.0

0.1

0.2

0.3

0.4

0.5

!100 !50 0 50 1000.0

0.1

0.2

0.3

0.4

0.5

!100 !50 0 50 1000.0

0.1

0.2

0.3

0.4

0.5

!50 0 50 1000.0

0.1

0.2

0.3

0.4

0.5

⏎


Giampiero Paffuti and Ken Konishi’s hobby: Quantum Mechanics

• Generalized uncertainty relations (string theory) ’90

• Cyclic oscillator theorem ’06 : Microscopic QM systems cannot act as engines

• New Quantum Mechanics book (800 p. + CD), Oxford Univ. Press (’09)

∆x =ℏ /∆p + ℷ ∆p ➯ Minimum physical length in Nature !

⏎


Physics of 2020

Be open mindedTuesday, April 12, 2011

24.1 Mathematical appendices 761

Table: Lepton masses

!e (eV) !µ (MeV) !! ( MeV)

< 3 < 0.19 < 18.2

e (MeV) µ (MeV) " (MeV)

0.51099892± 4 · 10!8 105.658369± 9 · 10!6 1776.99± 0.26

Table 24.9

Table: Gauge boson masses

photon gluons W± (GeV) Z (GeV)

0 0 80.425± 0.038 91.1876± 0.0021

Table 24.10

Table: Neutrino masses

!e !µ !!

!12 m2 = (6 ! 9) · 10!5 eV2

!23 m2 = (1 ! 3) · 10!3 eV2

Table 24.11 Solar neutrinos and reactor (SNO, SuperKamiokande, Kam-LAND) experiments give the first results. Atmospheric neutrino data andthe long baseline experiment (SuperKamiokande, K2K) provide the second.The mixing angle relevant to the solar and reactor neutrino oscillation is large,tan2 !12 ! 0.40+0.10

!0.07 , while the one related to the atmospheric neutrino data ismaximal, sin2 2!23 ! 1. Cosmological considerations give

P

m!i < O(1 eV).

760 Mathematical appendices and tables

Table: Quarks and their charges

Quarks SUL(2) UY (1) UEM (1)

!uL

d!L

",

!cL

s!L

",

!tLb!L

"2 1

3

!23

! 13

"

uR, cR, tR 1 43

23

dR, sR, bR 1 ! 23 ! 1

3

Table 24.6 The primes indicate that the mass eigenstates are di!erent fromthe states transforming as multiplets of SUL(2) ! UY (1). They are linearlyrelated by the Cabibbo–Kobayashi–Maskawa mixing matrix.

Table: Leptons and their charges

Leptons SUL(2) UY (1) UEM (1)

!!!

e LeL

",

!!!

µ L

µL

",

!!!

! L"L

"2 !1

!0!1

"

eR, µR, "R 1 !2 !1

Table 24.7 The primes indicate again that the mass eigenstates are di!erentfrom the states transforming as multiplets of SUL(2) ! UY (1), as required bythe observed neutrino oscillations.

Table: Quark masses

u (MeV) c (GeV) t (GeV) d (MeV) s (MeV) b (GeV)

1.5 ! 4 1.15 ! 1.35 174.3 ± 5.1 4 ! 8 80 ! 130 4.1 ! 4.4

Table 24.8



!e (eV) !µ (MeV) !! ( MeV)

< 3 < 0.19 < 18.2


0.51099892± 4 · 10!8 105.658369± 9 · 10!6 1776.99± 0.26

Table 24.9



0 0 80.425± 0.038 91.1876± 0.0021

Table 24.10


!e !µ !!

!12 m2 = (6 ! 9) · 10!5 eV2

!23 m2 = (1 ! 3) · 10!3 eV2



P

m!i < O(1 eV).



!e (eV) !µ (MeV) !! ( MeV)

< 3 < 0.19 < 18.2


0.51099892± 4 · 10!8 105.658369± 9 · 10!6 1776.99± 0.26

Table 24.9



0 0 80.425± 0.038 91.1876± 0.0021

Table 24.10


!e !µ !!

!12 m2 = (6 ! 9) · 10!5 eV2

!23 m2 = (1 ! 3) · 10!3 eV2



P

m!i < O(1 eV).


Remarks

• We are basically made of

p ! uud; n ! udd; e; !

i.e., of u, d, e, γ, gluons

• Nevertheless, baryogenesis (CKM quark mixing, CP violation, B-violation)

➩ all quarks, leptons and gauge bosons of the Table

for us to be here today

indispensable

B.T.W.

fundamental contributions by the experimental HE groups of Pisa

• the top quark discovery

• CP in K

• CP in B ⏎Tuesday, April 12, 2011

⏎

G.Morchio, F.Strocchi, C.Budroni (dottorando a Siviglia) Fondamenti della MQ e effetti non perturbativi in teorie di gauge

1. Algebre di Poisson non commutative, invarianza per diffeomorfismi e quantizzazione

Risultati: A) MQ sulle varietà differenziabili: Per ogni varietà M esiste unʼunica ∗ algebra A(M), generata dalle funzioni f su M e dalle traslazioni infinitesime Tv lungo tutti i campi vettoriali v, con le relazioni di commutazione di Lie tra funzioni e campi vettoriali e le relazioni di Lie-Rinehart Tf v = 1/2(f Tv + Tv f ) . A(M) è invariante per diffeomorfismi. Le relazioni di Lie-Rinehart sono essenziali per la non proliferazione dei gradi di libertà (associati allʼalgebra di Lie infinito dimensionale dei diffeomorfismi) Le rappresentazioni di A(M) sono tutte localmente Schroedinger (in generale con molteplici- tà) e sono classificate dal primo gruppo di omotopia π1(M ), che in generale non è commutativo e dà perciò origine a “fasi non abeliane”.

B) Derivazione della quantizzazione di Dirac senza inconsistenze:

A ogni varieta è associata lʼalgebra di Poisson delle funzioni e dei campi vettoriali, con le relazioni di Lie-Rinehart, senza altri vincoli su prodotti o commutatori. Tale algebra contiene una variabile centrale Z , che commuta e ha Poisson nullo con tutti gli el- ementi e che mette in relazione Poisson e commutatori: Tv f (x) − f (x)Tv = Z {Tv , f (x)}

Z = −Z ∗. Nelle rappresentazioni irriducibili

Soli risultati possibili: - c = 0: Meccanica Classica lagrangiana - Meccanica quantistica come sopra con c = i


theory group at dep. phys. “enrico fermi” · luc, lui, giam francesco (b): daniele ... an...

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