Temporally ordered graphs in quantum field theory

1955 ◽  
Vol 51 (1) ◽  
pp. 113-120 ◽  
Author(s):  
J. C. Polkinghorne
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Momentum Space ◽  
Transformation Operator ◽  
Time Interval ◽  
Quantum Field ◽  
Cayley Transform ◽  
Infinite Time ◽  
Infinite Time Interval ◽  
Ordered Graphs

ABSTRACTThe S matrix is expressed in terms of momentum-space operators and its Cayley transform exhibited. A new graphical formalism called O-graphs is developed in which the vertices are temporally ordered and the lines represent real particles. This is used to prove a conjecture of Gupta concerning the relation of real and virtual processes to the Cayley transform. The transformation operator for a semi-infinite time interval is also considered and some of its properties demonstrated. In conclusion, another graphical formalism with temporally ordered vertices is developed and renormalized.

scholarly journals The Dirac Sea, T and C Symmetry Breaking, and the Spinor Vacuum of the Universe

Universe ◽  
2021 ◽  
Vol 7 (5) ◽  
pp. 124
Author(s):  
Vadim Monakhov
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Symmetry Breaking ◽  
Momentum Space ◽  
Quantum Field ◽  
Conjugation Operator ◽  
Dirac Sea ◽  
Canonical Anticommutation Relations ◽  
The Universe ◽  
Dirac Conjugation

We have developed a quantum field theory of spinors based on the algebra of canonical anticommutation relations (CAR algebra) of Grassmann densities in the momentum space. We have proven the existence of two spinor vacua. Operators C and T transform the normal vacuum into an alternative one, which leads to the breaking of the C and T symmetries. The CPT is the real structure operator; it preserves the normal vacuum. We have proven that, in the theory of the Dirac Sea, the formula for the charge conjugation operator must contain an additional generalized Dirac conjugation operator.

Momentum space techniques for curved space–time quantum field theory

1979 ◽  
Vol 367 (1728) ◽  
pp. 123-141 ◽  
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Momentum Space ◽  
Nuclear Physics ◽  
Space Time ◽  
Coordinate Space ◽  
Quantum Field ◽  
Curved Space ◽  
Time Quantum ◽  
Space Formulation

A momentum space formulation of curved space–time quantum field theory is presented. Such a formulation allows the riches of momentum space calculational techniques already existing in nuclear physics to be exploited in the application of quantum field theory to cosmology and astrophysics. It is demonstrated that one such technique can allow exact, or very accu­rate approximate, results to be obtained in cases which are intractable in coordinate space. An efficient method of numerical solution is also described.

ON NON-ZERO MASS SOLUTIONS IN MASSLESS QUANTUM FIELD THEORY WITH CURVED MOMENTUM SPACE

2001 ◽  
Author(s):  
B. E. J. BODMANN ◽  
S. MITTMANN DOS SANTOS ◽  
TH. A. J. Maris
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Momentum Space ◽  
Quantum Field ◽  
Zero Mass ◽  
Massless Quantum

scholarly journals Quantum Field Theory with Finite Time Interval: Application to QED

1991 ◽  
Vol 86 (1) ◽  
pp. 269-302 ◽  
Author(s):  
K. Nomoto ◽  
R. Fukuda
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Finite Time ◽  
Time Interval ◽  
Quantum Field ◽  
Finite Time Interval

A quantum field theory in momentum space of constant curvature

1981 ◽  
Vol 24 (9) ◽  
pp. 796-800
Author(s):  
S. A. Gadzhiev ◽  
V. A. Petrosyan
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Constant Curvature ◽  
Momentum Space ◽  
Quantum Field ◽  
Space Of Constant Curvature

Singular Functions in Quantum Field Theory with De Sitter Momentum Space

1997 ◽  
Vol 12 (01) ◽  
pp. 255-258
Author(s):  
R. M. Mir-Kasimov
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Scalar Field ◽  
Explicit Form ◽  
Momentum Space ◽  
Legendre Functions ◽  
Quantum Field ◽  
De Sitter ◽  
Singular Functions ◽  
Positive Frequency

The positive frequency part of commutation Pauli-Jordan function in the Quantum Field Theory with curved momentum space or Quantum configurational space is calculated in explicit form for scalar field. The expressions for other siigular functions are also written in terms of Legendre functions

Momentum space of constant curvature and the ?rainbow? approximation in quantum field theory

1983 ◽  
Vol 26 (9) ◽  
pp. 798-802
Author(s):  
S. A. Gadzhiev ◽  
V. A. Petrosyan
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Constant Curvature ◽  
Momentum Space ◽  
Quantum Field ◽  
Space Of Constant Curvature
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