scholarly journals Link between quantum measurement and theiεterm in the quantum field theory propagator

2014 ◽  
Vol 90 (12) ◽  
Author(s):  
Roman Sverdlov ◽  
Luca Bombelli
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Measurement ◽  
Quantum Field

scholarly journals CLASSICAL ODE AND PDE WHICH OBEY QUANTUM DYNAMICS

2002 ◽  
Vol 12 (10) ◽  
pp. 2031-2049 ◽  
Author(s):  
PAUL J. WERBOS
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Computing ◽  
Quantum Measurement ◽  
Quantum Dynamics ◽  
Emergent Properties ◽  
Quantum Field ◽  
Superstring Theory ◽  
Classical Systems ◽  
Statistical Correlations

It is well known that classical systems governed by ODE or PDE can have extremely complex emergent properties. Many researchers have asked: is it possible that the statistical correlations which emerge over time in classical systems would allow effects as complex as those generated by quantum field theory (QFT)? For example, could parallel computation based on classical statistical correlations in systems based on continuous variables, distributed over space, possibly be as powerful as quantum computing based on entanglement? This paper proves that the answer to this question is essentially "yes," with certain caveats. More precisely, the paper shows that the statistics of many classical ODE and PDE systems obey dynamics remarkably similar to the Heisenberg dynamics of the corresponding quantum field theory (QFT). It supports Einstein's conjecture that much of quantum mechanics may be derived as a statistical formalism describing the dynamics of classical systems. Predictions of QFT result from combining quantum dynamics with quantum measurement rules. Bell's Theorem experiments which rule out "classical field theory" may therefore be interpreted as ruling out classical assumptions about measurement which were not part of the PDE. If quantum measurement rules can be derived as a consequence of quantum dynamics and gross thermodynamics, they should apply to a PDE model of reality just as much as they apply to a QFT model. This implies: (1) the real advantage of "quantum computing" lies in the exploitation of quantum measurement effects, which may have possibilities well beyond today's early efforts; (2) Lagrangian PDE models assuming the existence of objective reality should be reconsidered as a "theory of everything." This paper will review the underlying mathematics, prove the basic points, and suggest how a PDE-based approach might someday allow a finite, consistent unified field theory far simpler than superstring theory, the only known alternative to date.

A Review of Conformal Field Theory in 2D

2014 ◽  
Vol 6 (2) ◽  
pp. 1079-1105
Author(s):  
Rahul Nigam
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Conformal Field Theory ◽  
Statistical Mechanics ◽  
Critical Behavior ◽  
Verma Module ◽  
Virasoro Algebra ◽  
Quantum Field ◽  
Conformal Field ◽  
Insight Into

In this review we study the elementary structure of Conformal Field Theory in which is a recipe for further studies of critical behavior of various systems in statistical mechanics and quantum field theory. We briefly review CFT in dimensions which plays a prominent role for example in the well-known duality AdS/CFT in string theory where the CFT lives on the AdS boundary. We also describe the mapping of the theory from the cylinder to a complex plane which will help us gain an insight into the process of radial quantization and radial ordering. Finally we will develop the representation of the Virasoro algebra which is the well-known "Verma module".  

Some remarks on a deformed quantum field theory

2002 ◽  
Author(s):  
Marco Aurelio Do Rego Monteiro ◽  
V. B. Bezerra ◽  
E. M.F. Curado
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Field

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.

QLB for Quantum Many-Body and Quantum Field Theory

2018 ◽  
Author(s):  
Sauro Succi
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Mechanics ◽  
Quantum Computing ◽  
Single Particle ◽  
Body Problem ◽  
Three Dimensions ◽  
Quantum Field ◽  
Many Body ◽  
Quantum Particles

Chapter 32 expounded the basic theory of quantum LB for the case of relativistic and non-relativistic wavefunctions, namely single-particle quantum mechanics. This chapter goes on to cover extensions of the quantum LB formalism to the overly challenging arena of quantum many-body problems and quantum field theory, along with an appraisal of prospective quantum computing implementations. Solving the single particle Schrodinger, or Dirac, equation in three dimensions is a computationally demanding task. This task, however, pales in front of the ordeal of solving the Schrodinger equation for the quantum many-body problem, namely a collection of many quantum particles, typically nuclei and electrons in a given atom or molecule.

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