• Aucun résultat trouvé

Derive the equations of motion for the complex scalar field with the folowing action S= Z d4x ∂µφ ∂µφ∗−λ 2(φ φ∗−v2)2

N/A
N/A
Info
Télécharger
Protected

Academic year: 2022

Partager "Derive the equations of motion for the complex scalar field with the folowing action S= Z d4x ∂µφ ∂µφ∗−λ 2(φ φ∗−v2)2 "

Copied!
1
0
0

Chargement.... (Voir le texte intégral maintenant)

Texte intégral

(1)

Quantum field theory Exercises 6.

2005-12-05

•Exercise 6.1.

Derive the equations of motion for the complex scalar field with the folowing action S=

Z d4x

∂µφ ∂µφ∗−λ

2(φ φ∗−v2)2

.

•Exercise 6.2.

Check explicitly in the model of one scalar field with potentialV(φ) S=

Z d4x

1

2∂µφ ∂µφ−V(φ)

that the energy

E= Z

d3x

1

2φ˙2+1

2∂iφ ∂iφ+V(φ)

is conserved (dE/dt =0) on the equations of motion.

•Exercise 6.3.

Find the dimensions of scalar, spinor, and gauge fields in space-time of dimension d=4.

A useful starting point is the fact that dimension of action S is the dimension of the Plank’s constant, i.e. it is dimensionless in ¯h= 1 units. Repeat the anaysis in arbitrary number of dimensionsd, using actionS=RddxL with usual expressions for LagrangianL.

6

Références

Télécharger maintenant ( PDF - 1 Page - 53.88 KB )

Documents relatifs

Ω |φ(x) − φ(x ′ )| 2 dx dx ′ =

façon très formelle) omme l'équation de la haleur ave oeient de diusion. imaginaire (égal à

2 Visibility φ = 1 in FSYNC

The only difference between the fully synchronous model (i.e., FSYNC) and the semi-synchronous model (i.e., SSYNC) is that with the former ∀t ≥ 0, |R(t)| = k—i.e., every robot

1/2 u R α φ −φ U R u 0 R CωU U

Niveau : Quatrième année sciences techniques Cours 1 : Etude d’un filtre actif en régime sinusoïdal Professeur : Tawfik Baccari.. 1/2 Quatrième année sciences techniques:

On the relativistic KMS condition for the P (φ)2

The relativistic KMS condition introduced by Bros and Buchholz pro- vides a link between quantum statistical mechanics and quantum field theory.. We show that for the P (φ) 2 model

2 On pose φ :x 7→ kxk2−dK(x)2.Montrer que φ(x

Soit E un espace

Montrer que ∀φ∈F∗, g∗(φ) =f∗(A∗φ)

Montrer que f est égale au suprémum de ses minorantes anes continues.. En déduire que f est convexe et

Soit φ la fonction définie sur R

[r]

φ ::= c | φ ⇒ ψ | φ ∧ φ | φ ∨ φ | Xφ | Fφ | Gφ | φUφ | φRφ | ∃x φ where c denotes a linear constraint over molecular concentrations, their first derivative, and a set of variables x, including the Time variable.

We consider the fundamental problem of calibrating an ODE model with respect to a temporal logic specification of the behavior of the system, observed in experiments.. We are