Continuoussymmetry breaking

and Goldstonemodes

T T H K H to F P

Ginzburg LondonHamiltonian fr n 2

p Had fddx t ni tum t E IE mT b in

it For b pHhas fullglobalrotationsymmetry

in Yin space

but ground state is ferromagnetic

I e At TeTa appearance of longrangeorder

and is accompaniedby spontaneous symmetrybeating

ii Uniform Cie global spinrotations wit no

energy but requiresmotiveofwholesystem

A story varyyCin yea rotation into

mylittle energyform low energy

collectiveexutates

e.g magners shinbonesphonons

orI

PA

longitudetown

yspheremode amplitudemods

are Marniemx int

energymy

Grundythe breathing of a

continuoussymmetry

existenceof low energy

excitation

Goldstonemods

Goldstonemods have a dramatic influence on the

nature ofLro in ten dimensions

see this unit h 2 XY yes superftweb

Zz Hy ne I

T r r p Itdomainhalls

T CTe T

JIm it o

a.m in tis go

pHCOT p It t KIfth lgotI k

3 Doc epHCo

looks Gansin ht niteOCD is fainter 21

th mas ther are contraint an or enhgf

and this admit topologically non timid

field configurtsvortices

chpproximhi fr large To lieten T we assure

that the untruth In Zis small

tu d 2

0 is unconstrained

o o

L O ly OKs G y I Cdcx X

whe Fedex SdCx Coulomb pathsin d denim

Applying fans der

Goldindeux dotx IcdI SdXt dydxtsurfeau of a unitd diment bull

Sd 2got

TCE

dadIqni

d

2 dCd I

G d Sdt cont

Sr L oh 06557 2 Coto co 06,7

2 ni d ar d

Tidyx o low length

rule wt offoCx ocos I lost d 2 x o

ly div d 2drips de 2

WB denims d 32 the apps a short

byth rule or UV diverges In principle this

wld be controlledby modifyingthe Henthorn

at short length rub lattice regularisation

Hour since we knowtht this is an

implicit lathesent we knewthe diverges

is

unplyrid so we can neglect it

tonsequiesm D in reCeiLOCH deo.Dy

in expf I do ex oath

x

hi dazo de2

True Leo shouldapproach a file content

tf Jew fluctuates destoyd Lro

Mermin Waywthorn

Fer system withcontinuous

symmetry Cad

shot rangedinteraction then is he Lro in

denims da fo ay finitetemperature

That fluctuates duty Lno

D 2 is hmm as low critical demeim

fr disunitesymmetry low wilddenimD

Furillo Derivationof Sd

Volume and

Safe era S Sart

f dye Tide dr sandier

An f dt E't

Tik Sd If E

See2

ME

1et r

g drrd Er'stfft dear dr

If E rd 2 1 1