scholarly journals Scalar field Green functions on causal sets

2017 ◽  
Vol 34 (12) ◽  
pp. 124002 ◽  
Author(s):  
Nomaan X ◽  
Fay Dowker ◽  
Sumati Surya
Keyword(s):  
Scalar Field ◽  
Green Functions ◽  
Causal Sets

scholarly journals THE BOLTZMANN EQUATION IN SCALAR FIELD THEORY

1998 ◽  
Vol 13 (24) ◽  
pp. 4281-4288 ◽  
Author(s):  
F. T. BRANDT ◽  
J. FRENKEL ◽  
A. GUERRA
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Temperature Limit ◽  
Equation Of Motion ◽  
Green Functions ◽  
Static Case ◽  
Quantum Field ◽  
Scalar Field Theory ◽  
High Temperature Limit ◽  
Classical Transport

We derive the classical transport equation, in scalar field theory with a g2V(ϕ) interaction, from the equation of motion for the quantum field. We obtain a very simple, but iterative, expression for the effective action Γ which generates all the n-point Green functions in the high-temperature limit. An explicit and closed form is given for Γ in the static case.

scholarly journals Some exact solutions of reduced scalar Yukawa theory

1998 ◽  
Vol 76 (7) ◽  
pp. 523-537 ◽  
Author(s):  
J W Darewych
Keyword(s):  
Scalar Field ◽  
Vacuum State ◽  
Analytic Solutions ◽  
Green Functions ◽  
Yukawa Model ◽  
Complex Scalar ◽  
Complex Scalar Field ◽  
Three Body ◽  
Yukawa Theory ◽  
Body Case

The scalar Yukawa model, in which a complex scalar field, ϕ, interacts via a real scalar field, χ, is reduced by using covariant Green functions. It is shown that exact few-particle eigenstates of the truncated QFT Hamiltonian can be obtained in the Feshbach–Villars formulation if an unorthodox "empty" vacuum state is used. Analytic solutions for the two-body case are obtained for massless chion exchange in 3+1 dimensions and for massive chion exchange in 1+1 dimensions. Comparison is made to ladder Bethe–Salpeter, Feynman–Schwinger, and quasipotential results for massive chion exchange in 3+1. Equations for the three-body case are also obtained. PACS Nos.: 11.10.Ef, 11.10.Qr, and 03.70.+k

Free scalar field

2018 ◽  
Author(s):  
Michael Kachelriess
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Yukawa Potential ◽  
Casimir Effect ◽  
Scalar Particle ◽  
Integral Approach ◽  
Green Functions ◽  
Vacuum Fluctuations ◽  
Free Scalar ◽  
Physical Consequences

In this chapter, the path integral approach is extended from quantum mechanics to the simplest field theory containing a single real scalar field. First the generating functionals of (dis-) connected n-point Green functions are introduced, then the Feynman propagator of the scalar field is derived and causality is discussed. The exchange of a space-like scalar particle between two static sources is examined and it is shown that it leads to an attractive Yukawa potential. The Casimir effect is used to demonstrate that vacuum fluctuations have physical consequences.

scholarly journals From Green function to quantum field

2017 ◽  
Vol 14 (08) ◽  
pp. 1740007 ◽  
Author(s):  
Rafael D. Sorkin
Keyword(s):  
Scalar Field ◽  
Green Function ◽  
General Condition ◽  
Ground State ◽  
Wightman Function ◽  
Quantum Field ◽  
Causal Sets ◽  
Retarded Green Function ◽  
Spacetime Region ◽  
Zero Entropy

A pedagogical introduction to the theory of a Gaussian scalar field which shows firstly, how the whole theory is encapsulated in the Wightman function [Formula: see text] regarded abstractly as a two-index tensor on the vector space of (spacetime) field configurations, and secondly how one can arrive at [Formula: see text] starting from nothing but the retarded Green function [Formula: see text]. Conceiving the theory in this manner seems well suited to curved spacetimes and to causal sets. It makes it possible to provide a general spacetime region with a distinguished “vacuum” or “ground state”, and to recognize some interesting formal relationships, including a general condition on [Formula: see text] expressing zero-entropy or “purity”.

Sign in / Sign up

Export Citation Format

Share Document