On the inequivalent representations of canonical commutation relations in quantum field theory

1963 ◽  
Vol 30 (3) ◽  
pp. 803-829 ◽  
Author(s):  
W. Weidlich
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Field ◽  
Canonical Commutation Relations ◽  
Commutation Relations ◽  
Inequivalent Representations

Some quantum field theory aspects of the superspace quantization of general relativity

1976 ◽  
Vol 351 (1665) ◽  
pp. 209-232 ◽  
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
General Relativity ◽  
Perturbation Theory ◽  
Constraint Equation ◽  
Mathematical Structure ◽  
Quantum Field ◽  
Canonical Commutation Relations ◽  
Commutation Relations ◽  
The Status

An investigation is started into a possible mathematical structure of the Wheeler-DeWitt superspace quantization of general relativity. The emphasis is placed throughout on quantum field theory aspects of the problem and topics discussed include canonical commutation relations in a triad basis, the status of the constraint equation and the rôle played by perturbation theory.

On the Feynman principle

1955 ◽  
Vol 230 (1181) ◽  
pp. 272-276 ◽  
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Equations Of Motion ◽  
Canonical Formalism ◽  
Quantum Field ◽  
Usual Definition ◽  
Canonical Commutation Relations ◽  
Commutation Relations ◽  
Feynman Amplitudes ◽  
Definition Of

The formulation of quantum field theory in terms of the Feynman principle is discussed. It is shown that the operators defined in terms of this principle satisfy the equations of motion. A definition of canonically conjugate momenta is given in terms of the principle and is shown to be equivalent to the usual definition. The canonical commutation relations are then deduced and the equivalence of this formulation and the canonical formalism is thereby established. The equations for Feynman amplitudes are also obtained. In conclusion some difficulties of the theory and some possible extensions are discussed.

scholarly journals ON FINITE NONCOMMUTATIVITY IN QUANTUM FIELD THEORY

2010 ◽  
Vol 25 (15) ◽  
pp. 2955-2964
Author(s):  
MIKLOS LÅNGVIK ◽  
ALI ZAHABI
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Exponential Function ◽  
Star Product ◽  
Integral Kernel ◽  
New Product ◽  
Quantum Field ◽  
Finite Range ◽  
Moyal Product ◽  
Commutation Relations

We consider various modifications of the Weyl–Moyal star-product, in order to obtain a finite range of nonlocality. The basic requirements are to preserve the commutation relations of the coordinates as well as the associativity of the new product. We show that a modification of the differential representation of the Weyl–Moyal star-product by an exponential function of derivatives will not lead to a finite range of nonlocality. We also modify the integral kernel of the star-product introducing a Gaussian damping, but find a nonassociative product which remains infinitely nonlocal. We are therefore led to propose that the Weyl–Moyal product should be modified by a cutoff-like function, in order to remove the infinite nonlocality of the product. We provide such a product, but it appears that one has to abandon the possibility of analytic calculation with the new product.

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