SCHWINGER α-PARAMETRIC REPRESENTATION OF FINITE TEMPERATURE FIELD THEORIES: RENORMALIZATION

1990 ◽  
Vol 05 (23) ◽  
pp. 4427-4440 ◽  
Author(s):  
M. BENHAMOU ◽  
A. KASSOU-OU-ALI
Keyword(s):  
Temperature Field ◽  
Scalar Field ◽  
Finite Temperature ◽  
Short Range ◽  
Parametric Representation ◽  
Field Theories ◽  
Compact Form ◽  
Zero Temperature ◽  
Feynman Amplitudes ◽  
Temperature Scalar

We present the extension of the zero temperature Schwinger α-representation to the finite temperature scalar field theories. We give, in a compact form, the α-integrand of Feynman amplitudes of these theories. Using this representation, we analyze short-range divergences, and recover in a simple way the known result that the counterterms are temperature-independent.

THE SCHWINGER α-PARAMETRIC REPRESENTATION OF THE FINITE-TEMPERATURE FIELD THEORY: RENORMALIZATION II

1992 ◽  
Vol 07 (01) ◽  
pp. 193-200
Author(s):  
MABROUK BENHAMOU ◽  
AHMED KASSOU-OU-ALI
Keyword(s):  
Field Theory ◽  
Temperature Field ◽  
Theta Function ◽  
Finite Temperature ◽  
Parametric Representation ◽  
Field Theories ◽  
Zero Temperature ◽  
Scalar Theory ◽  
Charged Scalar ◽  
Finite Temperature Field Theory

We extend to finite-temperature field theories, involving charged scalar or nonvanishing spin particles, the α parametrization of field theories at zero temperature. This completes a previous work concerning the scalar theory. As there, a function θ, which contains all temperature dependence, appears in the α integrand. The function θ is an extension of the usual theta function. The implications of the α parametrization for the renormalization problem are discussed.

scholarly journals ASYMPTOTIC EXPANSIONS OF FEYNMAN AMPLITUDES IN A GENERIC COVARIANT GAUGE

2008 ◽  
Vol 23 (07) ◽  
pp. 1089-1103
Author(s):  
C. A. LINHARES ◽  
A. P. C. MALBOUISSON ◽  
I. RODITI
Keyword(s):  
Scalar Field ◽  
Asymptotic Expansions ◽  
Gauge Theories ◽  
Present Situation ◽  
Parametric Representation ◽  
Field Theories ◽  
Covariant Gauge ◽  
Feynman Amplitudes ◽  
Mellin Representation

We show in this paper how to construct Symanzik polynomials and the Schwinger parametric representation of Feynman amplitudes for gauge theories in a generic covariant gauge. The complete Mellin representation of such amplitudes is then established in terms of invariants (squared sums of external momenta and squared masses). From the scaling of the invariants by a parameter we extend for the present situation a theorem on asymptotic expansions, previously proven for the case of scalar field theories, valid for both ultraviolet or infrared behaviors of Feynman amplitudes.

scholarly journals Cutting Rules at Finite Temperature

1997 ◽  
Vol 12 (33) ◽  
pp. 2481-2496 ◽  
Author(s):  
Paulo F. Bedaque ◽  
Ashok Das ◽  
Satchidananda Naik
Keyword(s):  
Field Theory ◽  
Temperature Field ◽  
Real Time ◽  
Imaginary Part ◽  
Physical Interpretation ◽  
Finite Temperature ◽  
Zero Temperature ◽  
Finite Temperature Field Theory ◽  
The Real

We discuss the cutting rules in the real-time approach to finite temperature field theory and show the existence of cancellations among classes of cut graphs which allows a physical interpretation of the imaginary part of the relevant amplitude in terms of the underlying microscopic processes. Furthermore, with these cancellations, any calculation of the imaginary part of an amplitude becomes much easier and completely parallel to the zero temperature case.

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