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

2019 ◽  
Vol 34 (23) ◽  
pp. 1950186 ◽  
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.

ON THE RELATION BETWEEN QUANTUM HYDRODYNAMICS AND CONVENTIONAL QUANTUM FIELD THEORY

1954 ◽  
Vol 32 (8) ◽  
pp. 530-537
Author(s):  
F. A. Kaempffer
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Wave Function ◽  
Classical Theory ◽  
Quantum Field ◽  
Quantum Hydrodynamics ◽  
Quantization Procedure ◽  
Nonrelativistic Theory ◽  
Hydrodynamical Description ◽  
Charged Medium

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.

scholarly journals Logarithmic expansion of field theories: higher orders and resummations

2021 ◽  
Vol 81 (6) ◽  
Author(s):  
Vincenzo Branchina ◽  
Alberto Chiavetta ◽  
Filippo Contino
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Finite Order ◽  
Weak Coupling ◽  
Field Theories ◽  
Quantum Field ◽  
First Order ◽  
Free Theory ◽  
Formal Expansion ◽  
The Way

AbstractA formal expansion for the Green’s functions of a quantum field theory in a parameter $$\delta $$ δ that encodes the “distance” between the interacting and the corresponding free theory was introduced in the late 1980s (and recently reconsidered in connection with non-hermitian theories), and the first order in $$\delta $$ δ was calculated. In this paper we study the $${\mathcal {O}}(\delta ^2)$$ O ( δ 2 ) systematically, and also push the analysis to higher orders. We find that at each finite order in $$\delta $$ δ the theory is non-interacting: sensible physical results are obtained only resorting to resummations. We then perform the resummation of UV leading and subleading diagrams, getting the $${\mathcal {O}}(g)$$ O ( g ) and $${\mathcal {O}}(g^2)$$ O ( g 2 ) weak-coupling results. In this manner we establish a bridge between the two expansions, provide a powerful and unique test of the logarithmic expansion, and pave the way for further studies.

scholarly journals Quantum Ostrogradsky theorem

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Hayato Motohashi ◽  
Teruaki Suyama
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Field ◽  
First Order ◽  
Higher Derivative ◽  
Original Theorem ◽  
Classical Lagrangian

Abstract The Ostrogradsky theorem states that any classical Lagrangian that contains time derivatives higher than the first order and is nondegenerate with respect to the highest-order derivatives leads to an unbounded Hamiltonian which linearly depends on the canonical momenta. Recently, the original theorem has been generalized to nondegeneracy with respect to non-highest-order derivatives. These theorems have been playing a central role in construction of sensible higher-derivative theories. We explore quantization of such non-degenerate theories, and prove that Hamiltonian is still unbounded at the level of quantum field theory.

A twistor approach to the regularization of divergences

1985 ◽  
Vol 397 (1813) ◽  
pp. 341-374 ◽  
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Infrared Divergence ◽  
Standard Theory ◽  
Quantum Field ◽  
New Formalism ◽  
First Order ◽  
Finite Theory ◽  
Finite Quantity ◽  
Modified Theory

One object of the twistor programme, as developed principally by R. Penrose, is the production of a manifestly finite theory of scattering in quantum field theory. Earlier work has shown that progress towards this goal is obstructed even at the first-order level, by the appearance of an infrared divergence in the standard theory. New studies in many-dimensional contour integration now suggest a simple but very powerful modification to this branch of twistor theory, in which the full (as opposed to the projective) twistor space plays an essential role. In this modified theory there arise natural contour-integral expressions with the effect of eliminating the infrared divergence previously noted, and replacing it by a finite quantity. This regularization can be specified by using a formalism of ‘inhomogeneous twistor diagrams’. The interpretation of this new formalism is not yet wholly clear, but the inhomogeneity can be seen as a means of relinquishing the concept of space-time point, while preserving light-cone structure. It therefore suggests a quite fresh approach to the divergences of quantum field theory.

A stochastic variational treatment of quantum mechanics

1995 ◽  
Vol 450 (1939) ◽  
pp. 417-437 ◽  
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.

scholarly journals Localization in quantum field theory

2017 ◽  
Vol 14 (08) ◽  
pp. 1740008 ◽  
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.

ON SOME PROPERTIES OF A MESON

2002 ◽  
Vol 17 (32) ◽  
pp. 4939-4945 ◽  
Author(s):  
S. N. BANERJEE ◽  
A. BHATTACHARYA ◽  
B. CHAKRABARTI ◽  
S. BANERJEE
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Free Energy ◽  
Wave Function ◽  
Gauge Symmetry ◽  
Symmetry Breaking ◽  
Statistical Model ◽  
Quantum Field ◽  
Condensate Wave Function ◽  
Fractal Properties

The free energy analyzed in the framework of the quantum field theory in conjunction with the statistical model for a [Formula: see text] meson is found to undergo an expansion in the condensate wave function. The superconducting and fractal properties of the meson are found to originate from the branch-cut type of singularity in the wave function of the model in which the gauge symmetry breaking is manifest.

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