Derivation of Equal-Time Commutation Relations in a Self-Consistent Quantum Field Theory

1971 ◽  
Vol 3 (8) ◽  
pp. 1890-1897 ◽  
Author(s):  
J. Rest ◽  
V. Srinivasan ◽  
H. Umezawa
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Field ◽  
Equal Time ◽  
Commutation Relations ◽  
Self Consistent ◽  
Equal Time Commutation

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.

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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