Obtaining the non-relativistic quantum mechanics from quantum field theory: issues, folklores and facts

  title={Obtaining the non-relativistic quantum mechanics from quantum field theory: issues, folklores and facts},
  author={Thanu Padmanabhan},
  journal={The European Physical Journal C},
Given the classical dynamics of a non-relativistic particle in terms of a Hamiltonian or an action, it is relatively straightforward to obtain the non-relativistic quantum mechanics (NRQM) of the system. These standard procedures, based on either the Hamiltonian or the path integral, however, do not work in the case of a relativistic particle. As a result we do not have a single-particle description of relativistic quantum mechanics (RQM). Instead, the correct approach requires a transmutation… Expand
Impact of relativity on particle localizability and ground state entanglement
Can a relativistic quantum field theory be consistently described as a theory of localizable particles? There are many known issues with such a description, indicating an answer in the negative. InExpand
From Quantum Field Theory to Quantum Mechanics
We construct the algebra of operators acting on the Hilbert spaces of Quantum Mechanics for systems of N identical particles from the field operators acting in the Fock space of Quantum Field TheoryExpand
Fakeons, quantum gravity and the correspondence principle
The correspondence principle made of unitarity, locality and renormalizability has been very successful in quantum field theory. Among the other things, it helped us build the standard model.Expand
Path integral of the relativistic point particle in Minkowski space
In this article, we analyze the fundamental global and local symmetries involved in the action for the free relativistic point particle in Minkowski space. Moreover, we identify a hidden localExpand
Path integrals for the relativistic particle: Some conceptual and pedagogical comments
In my textbook on Quantum Field Theory \cite{tpqft} and in a recent paper \cite{tpejc2018}, I advocated a lattice regularization procedure for defining the path integral for the relativisticExpand
Thermality of the Rindler horizon: A simple derivation from the structure of the inertial propagator
The Feynman propagator G(x1,x2) encodes all of the physics contained in a free field and transforms as a covariant biscalar. Therefore, we should be able to discover the thermality of the RindlerExpand
A measure for quantum paths, gravity and spacetime microstructure
The number of classical paths of a given length, connecting any two events in a (pseudo) Riemannian spacetime is, of course, infinite. It is, however, possible to define a useful, finite, measureExpand
Schwinger pair production in hot anti-de Sitter space
We consider particle production in $1+1$ dimensional thermal Anti-de Sitter space under the influence of a constant electric field. The vacuum-persistence amplitude is given by a non-relativisticExpand
Probing the Planck scale: the modification of the time evolution operator due to the quantum structure of spacetime
The propagator which evolves the wave-function in NRQM, can be expressed as a matrix element of a time evolution operator: i.e $ G_{\rm NR}(x)= \langle{\mathbf{x}_2}|{U_{\rmExpand


Relativistic quantum mechanics and relativistic entanglement in the rest-frame instant form of dynamics
A new formulation of relativistic quantum mechanics is proposed in the framework of the rest-frame instant form of dynamics, where the world-lines of the particles are parametrized in terms of theExpand
A New Approach to The Quantum Mechanics
In this paper, we try to give a new approach to the quantum mechanics(QM) on the framework of quantum field theory(QFT). Firstly, we make a detail study on the (non-relativistic) Schr\"odinger fieldExpand
Relativistic quantum mechanics of supersymmetric particles
The quantum mechanics of an electron in an external field is developed by Hamiltonian path integral methods. The electron is described classically by an action which is invariant under gaugeExpand
Localization in Relativistic Quantum Theories
Although the concept of localization in non-relativistic quantum mechanics is mathematically well-defined there is no obvious and unambiguous way to generalize it to relativistic quantum theory.Expand
On relativistic entanglement and localization of particles and on their comparison with the nonrelativistic theory
We make a critical comparison of relativistic and nonrelativistic classical and quantum mechanics of particles in inertial frames as well of the open problems in particle localization at both levels.Expand
The simple physics of a free particle reveals important features of the path-integral formulation of relativistic quantum theories. The exact quantum-mechanical propagator is calculated here for aExpand
Relativistic Quantum Mechanics
Introduction and some problems encountered in the construction of a relativistic quantum theory.- Relativistic Classical and Quantum Mechanics.- Spin, Statistics and Correlations.- Gauge Fields andExpand
Quantum mechanics of the gravitational field
An approach to the quantum theory of gravitation is developed by analogy with the quantum mechanics of the simplest generally covariant system: the relativistic point particle. The central object inExpand
Decoherent histories analysis of the relativistic particle
The Klein-Gordon equation is a useful test arena for quantum cosmological models described by the Wheeler-DeWitt equation. We use the decoherent histories approach to quantum theory to obtain theExpand
Sum-over-histories origin of the composition laws of relativistic quantum mechanics and quantum cosmology.
  • Halliwell, Ortíz
  • Physics, Medicine
  • Physical review. D, Particles and fields
  • 1993
The principal technical aim of this paper is to show that the relativistic composition law may, in fact, be derived directly from a sum over histories by partitioning the paths according to their first crossing position of an intermediate surface. Expand