scholarly journals A Class of Representations of the ∗-Algebra of the Canonical Commutation Relations over a Hilbert Space and Instability of Embedded Eigenvalues in Quantum Field Models

1997 ◽  
Vol 4 (3-4) ◽  
pp. 338-349 ◽  
Author(s):  
Asao Arai
Keyword(s):  
Hilbert Space ◽  
Quantum Field ◽  
Canonical Commutation Relations ◽  
Commutation Relations ◽  
Embedded Eigenvalues

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.

QUANTUM FIELD THEORETICAL FORMULATION OF EQUATION OF STATE FOR FERMION–BOSON MIXTURES

2003 ◽  
Vol 17 (31n32) ◽  
pp. 5943-5949
Author(s):  
DAISUKE ANMA ◽  
KEN-ICHI TAKIUCHI ◽  
TADASHI TOYODA
Keyword(s):  
Equation Of State ◽  
Scale Transformation ◽  
Quantum Field ◽  
Boson Systems ◽  
Theoretical Formulation ◽  
Equal Time ◽  
Canonical Commutation Relations ◽  
Commutation Relations ◽  
Canonical Generator

Using a quantum field theoretical canonical generator for the scale transformation of the second quantized Schrödinger fields describing a mixture of Fermion and Boson systems, the equation of state is derived. The derivation is based on the equal-time canonical commutation relations of the field operators and no approximation is employed. The result can be applied to liquid 3 He –4 He mixture.

scholarly journals Singular Bogoliubov transformations and inequivalent representations of canonical commutation relations

2019 ◽  
Vol 31 (08) ◽  
pp. 1950026 ◽  
Author(s):  
Asao Arai
Keyword(s):  
Fock Space ◽  
Sufficient Conditions ◽  
Bogoliubov Transformation ◽  
Fock Representation ◽  
Canonical Commutation Relations ◽  
Commutation Relations ◽  
Direct Sum ◽  
Boson Fock Space ◽  
Inequivalent Representations ◽  
Bogoliubov Transformations

We introduce a concept of singular Bogoliubov transformation on the abstract boson Fock space and construct a representation of canonical commutation relations (CCRs) which is inequivalent to any direct sum of the Fock representation. Sufficient conditions for the representation to be irreducible are formulated. Moreover, an example of such representations of CCRs is given.

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