Reply to “Comment on ‘Relation between scattering amplitude and Bethe-Salpeter wave function in quantum field theory”’

The conditions are examined under which the procedure of quantum hydrodynamics would be a consequence of the conventional quantization procedure, and vice versa. Using the classical nonrelativistic theory of a charged medium as an example, it is shown that the commutation rules of the two procedures differ by a factor 2, if in accordance with an idea by Geilikman the wave function of the classical theory is expanded as ψ = ψ0 + ψ1, with ψ0 a constant and [Formula: see text], and if terms of higher than second order in ψ1 are neglected in the hydrodynamical description of the theory.

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A novel view on successive quantizations, leading to increasingly more “miraculous” states

Modern Physics Letters A ◽

10.1142/s0217732319501861 ◽

2019 ◽

Vol 34 (23) ◽

pp. 1950186 ◽

Cited By ~ 1

Author(s):

Matej Pavšič

Keyword(s):

Field Theory ◽

Quantum Field Theory ◽

Wave Function ◽

Wave Packet ◽

Time Derivative ◽

Point Particle ◽

Order Equation ◽

Quantum Field ◽

First Order ◽

Complex Wave

A series of successive quantizations is considered, starting with the quantization of a non-relativistic or relativistic point particle: (1) quantization of a particle’s position, (2) quantization of wave function, (3) quantization of wave functional. The latter step implies that the wave packet profiles forming the states of quantum field theory are themselves quantized, which gives new physical states that are configurations of configurations. In the procedure of quantization, instead of the Schrödinger first-order equation in time derivative for complex wave function (or functional), the equivalent second-order equation for its real part was used. In such a way, at each level of quantization, the equation a quantum state satisfies is just like that of a harmonic oscillator, and wave function(al) is composed in terms of the pair of its canonically conjugated variables.

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𝒫𝒯-symmetric quantum field theory on the noncommutative spacetime

Modern Physics Letters A ◽

10.1142/s0217732320500121 ◽

2019 ◽

Vol 35 (05) ◽

pp. 2050012

Author(s):

Oleg O. Novikov

Keyword(s):

Field Theory ◽

Quantum Field Theory ◽

Scattering Amplitude ◽

Quantum Field ◽

Leading Order ◽

Symmetric Quantum ◽

Noncommutative Spacetime ◽

T Matrix ◽

The One ◽

New Formula

We consider the [Formula: see text]-symmetric quantum field theory on the noncommutative spacetime with angular twist and construct its pseudo-Hermitian interpretation. We explore the differences between internal and spatial parities in the context of the angular twist and for the latter we find new [Formula: see text]-symmetric interactions that are nontrivial only for the noncommutative spacetime. We reproduce the same formula for the leading order T-matrix of the equivalent Hermitian model as the one obtained earlier for the quantum field theory on the commutative spacetime. This formula implies that the leading order scattering amplitude preserves the symmetries of the noncommutative geometry if they are not broken in the non-Hermitian formulation.

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A stochastic variational treatment of quantum mechanics

Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences ◽

10.1098/rspa.1995.0092 ◽

1995 ◽

Vol 450 (1939) ◽

pp. 417-437 ◽

Cited By ~ 13

Keyword(s):

Field Theory ◽

Quantum Field Theory ◽

Wave Function ◽

Quantum Mechanics ◽

Standard Theory ◽

Quantum Field ◽

Extended Form ◽

Variational Treatment ◽

Close Relationship ◽

Methods Of Control

An earlier development of some results in quantum mechanics from a stochastic variational principle is extended in several directions. An outline is first given of the methods of control theory upon which the development is based, and earlier results are briefly described. Extensions are then given to relativistic systems, to Dirac’s equation, and to elementary quantum field theory. The aim thoughout is to show that results in the standard theory can be obtained in a uniform way from an extended form of Hamilton’s principle, which has the advantage of conciseness and a relatively close relationship to the classical theory. The wave function appears as a modified form of the optimal cost function, and the photon can be identified with a singularity in the electromagnetic field. Interference is explained by optimization of an expected value, the ensemble over which the expectation is taken being dependent upon the information available.

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Localization in quantum field theory

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887817400084 ◽

2017 ◽

Vol 14 (08) ◽

pp. 1740008 ◽

Cited By ~ 1

Author(s):

A. P. Balachandran

Keyword(s):

Field Theory ◽

Quantum Field Theory ◽

Wave Function ◽

Black Hole Physics ◽

Relativistic Quantum ◽

Relativistic Quantum Mechanics ◽

Unruh Effect ◽

Quantum Field ◽

Simple Derivation ◽

Spatial Region

In non-relativistic quantum mechanics, Born’s principle of localization is as follows: For a single particle, if a wave function [Formula: see text] vanishes outside a spatial region [Formula: see text], it is said to be localized in [Formula: see text]. In particular, if a spatial region [Formula: see text] is disjoint from [Formula: see text], a wave function [Formula: see text] localized in [Formula: see text] is orthogonal to [Formula: see text]. Such a principle of localization does not exist compatibly with relativity and causality in quantum field theory (QFT) (Newton and Wigner) or interacting point particles (Currie, Jordan and Sudarshan). It is replaced by symplectic localization of observables as shown by Brunetti, Guido and Longo, Schroer and others. This localization gives a simple derivation of the spin-statistics theorem and the Unruh effect, and shows how to construct quantum fields for anyons and for massless particles with “continuous” spin. This review outlines the basic principles underlying symplectic localization and shows or mentions its deep implications. In particular, it has the potential to affect relativistic quantum information theory and black hole physics.

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