Von Hove model of quantum field theory‐from the point of view of infinite dimensional stationary Markov process theory

1992 ◽  
Vol 33 (3) ◽  
pp. 1127-1131
Author(s):  
Zheng Dong Wang
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Markov Process ◽  
Point Of View ◽  
Process Theory ◽  
Quantum Field ◽  
Infinite Dimensional ◽  
Stationary Markov Process

scholarly journals Infinite dimensional Langevin equation and Fokker-Planck equation

1981 ◽  
Vol 81 ◽  
pp. 177-223 ◽  
Author(s):  
Yoshio Miyahara
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Hilbert Space ◽  
Partial Differential Equations ◽  
Langevin Equation ◽  
Planck Equation ◽  
Theory Theory ◽  
Quantum Field ◽  
Filtering Theory ◽  
Infinite Dimensional

Stochastic processes on a Hilbert space have been discussed in connection with quantum field theory, theory of partial differential equations involving random terms, filtering theory in electrical engineering and so forth, and the theory of those processes has greatly developed recently by many authors (A. B. Balakrishnan [1, 2], Yu. L. Daletskii [7], D. A. Dawson [8, 9], Z. Haba [12], R. Marcus [18], M. Yor [26]).

A Possible Role of Universal Length in the Theory of Weak Interactions

1973 ◽  
Vol 51 (14) ◽  
pp. 1577-1581 ◽  
Author(s):  
D. Y. Kim
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Weak Interactions ◽  
Relativistic Quantum ◽  
Universal Constant ◽  
Point Of View ◽  
Quantum Field ◽  
Elementary Length ◽  
Modern Physics

The discovery and role of already existing universal constants h and c in modern physics have been reviewed from a particular point of view. This viewpoint is characterized by a pattern of logic in terms of which one may possibly find a new universal constant, i.e. the elementary length. One of the main objectives of this paper is to find out whether the elementary length introduced this way would resolve inherent difficulties in relativistic quantum field theory. This has been explicitly studied in terms of the nonlocal field theory in connection with the CP violating kaon decay. This produced a relation [Formula: see text] which leads, on the one hand, to a consistent explanation of the possible mechanism of CP violation and, on the other hand, gives a result which is most probably the first direct link between the elementary length (nonlocality) and an experiment without having the inherent disorder in the small distance behavior in quantum field theory.

scholarly journals Area-Dependent Quantum Field Theory

2020 ◽  
Author(s):  
Ingo Runkel ◽  
Lóránt Szegedy
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Field ◽  
Two Dimensional ◽  
Positive Real ◽  
Yang Mills ◽  
Infinite Dimensional ◽  
Frobenius Algebras ◽  
Topological Quantum ◽  
Topological Theories

AbstractArea-dependent quantum field theory is a modification of two-dimensional topological quantum field theory, where one equips each connected component of a bordism with a positive real number—interpreted as area—which behaves additively under glueing. As opposed to topological theories, in area-dependent theories the state spaces can be infinite-dimensional. We introduce the notion of regularised Frobenius algebras in Hilbert spaces and show that area-dependent theories are in one-to-one correspondence to commutative regularised Frobenius algebras. We also provide a state sum construction for area-dependent theories. Our main example is two-dimensional Yang–Mills theory with compact gauge group, which we treat in detail.

On the "Edge of the Wedge" Theorem

1963 ◽  
Vol 15 ◽  
pp. 125-131 ◽  
Author(s):  
Felix E. Browder
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Complex Variables ◽  
Point Of View ◽  
Several Complex Variables ◽  
Quantum Field ◽  
Complete Proof ◽  
Strategic Role ◽  
Mathematical Justification ◽  
Axiomatic Quantum Field Theory

In the mathematical justification of the formal calculations of axiomatic quantum field theory and the theory of dispersion relations, a strategic role is played by a theorem on analytic functions of several complex variables which has been given the euphonious name of the edge of the wedge theorem. The statement of the theorem seems to be due originally to N. Bogoliubov (cf. 3, Mathematical Appendix, pp. 654-673) but no complete proof which is fully satisfactory from the mathematical point of view has yet appeared in the literature.

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