Einstein's Dissatisfaction with Nonrelativistic Quantum Mechanics and Relativistic Quantum Field Theory

2010 ◽  
Vol 77 (5) ◽  
pp. 1042-1057 ◽  
Author(s):  
Miklós Rédei
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Mechanics ◽  
Relativistic Quantum ◽  
Quantum Field ◽  
Nonrelativistic Quantum ◽  
Relativistic Quantum Field Theory ◽  
Nonrelativistic Quantum Mechanics

Perturbation Expansion: Is it Asymptotic?

1997 ◽  
Vol 12 (32) ◽  
pp. 2399-2406 ◽  
Author(s):  
Kunio Yamamoto
Keyword(s):  
Field Theory ◽  
Relativistic Quantum ◽  
Perturbation Expansion ◽  
Bound State ◽  
Quantum Field ◽  
Nonrelativistic Quantum ◽  
Relativistic Quantum Field Theory ◽  
Physical Amplitude ◽  
Feynman Rules ◽  
Nonrelativistic Quantum Mechanics

It is pointed out that, for any model with bound state, contrary to the case of nonrelativistic quantum mechanics, perturbation expansion based on Feynman rules in relativistic quantum field theory is not asymptotic of physical amplitude in which the effects of bound state are considered.

scholarly journals Time in Quantum Mechanics and the Local Non-Conservation of the Probability Current

Mathematics ◽  
2018 ◽  
Vol 6 (9) ◽  
pp. 155 ◽  
Author(s):  
Giovanni Modanese
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Relativistic Quantum ◽  
Quantum Field ◽  
Relativistic Quantum Field Theory ◽  
Non Local ◽  
Time In Quantum Mechanics

In relativistic quantum field theory with local interactions, charge is locally conserved. This implies local conservation of probability for the Dirac and Klein–Gordon wavefunctions, as special cases; and in turn for non-relativistic quantum field theory and for the Schrödinger and Ginzburg–Landau equations, regarded as low energy limits. Quantum mechanics, however, is wider than quantum field theory, as an effective model of reality. For instance, fractional quantum mechanics and Schrödinger equations with non-local terms have been successfully employed in several applications. The non-locality of these formalisms is strictly related to the problem of time in quantum mechanics. We explicitly compute, for continuum wave packets, the terms of the fractional Schrödinger equation and the non-local Schrödinger equation by Lenzi et al. that break local current conservation. Additionally, we discuss the physical significance of these terms. The results are especially relevant for the electromagnetic coupling of these wavefunctions. A connection with the non-local Gorkov equation for superconductors and their proximity effect is also outlined.

Quantum mechanics

2018 ◽  
Author(s):  
Michael Kachelriess
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Mechanics ◽  
Relativistic Quantum ◽  
Transition Amplitude ◽  
External Source ◽  
Quantum Field ◽  
Damping Term ◽  
Relativistic Quantum Theory ◽  
Generating Functional

After a brief review of the operator approach to quantum mechanics, Feynmans path integral, which expresses a transition amplitude as a sum over all paths, is derived. Adding a linear coupling to an external source J and a damping term to the Lagrangian, the ground-state persistence amplitude is obtained. This quantity serves as the generating functional Z[J] for n-point Green functions which are the main target when studying quantum field theory. Then the harmonic oscillator as an example for a one-dimensional quantum field theory is discussed and the reason why a relativistic quantum theory should be based on quantum fields is explained.

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