scholarly journals A path integral formulation for particle detectors: the Unruh-DeWitt model as a line defect

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Ivan M. Burbano ◽  
T. Rick Perche ◽  
Bruno de S. L. Torres
Keyword(s):  
Path Integral ◽  
Degrees Of Freedom ◽  
Wilson Line ◽  
Transition Probability ◽  
Relativistic Quantum ◽  
Quantum Fields ◽  
Line Defect ◽  
Particle Detectors ◽  
Nonlocal Operators ◽  
Detector Model

Abstract Particle detectors are an ubiquitous tool for probing quantum fields in the context of relativistic quantum information (RQI). We formulate the Unruh-DeWitt (UDW) particle detector model in terms of the path integral formalism. The formulation is able to recover the results of the model in general globally hyperbolic spacetimes and for arbitrary detector trajectories. Integrating out the detector’s degrees of freedom yields a line defect that allows one to express the transition probability in terms of Feynman diagrams. Inspired by the light-matter interaction, we propose a gauge invariant detector model whose associated line defect is related to the derivative of a Wilson line. This is another instance where nonlocal operators in gauge theories can be interpreted as physical probes for quantum fields.

scholarly journals DISTILLABILITY AND POSITIVITY OF PARTIAL TRANSPOSES IN GENERAL QUANTUM FIELD SYSTEMS

2005 ◽  
Vol 17 (05) ◽  
pp. 545-576 ◽  
Author(s):  
RAINER VERCH ◽  
REINHARD F. WERNER
Keyword(s):  
Degrees Of Freedom ◽  
Field Model ◽  
Relativistic Quantum ◽  
Vacuum State ◽  
Quantum Systems ◽  
Quantum Field ◽  
Quantum Fields ◽  
Relativistic Quantum Field Theory ◽  
Positive Partial Transpose ◽  
Partial Transpose

Criteria for distillability, and the property of having a positive partial transpose, are introduced for states of general bipartite quantum systems. The framework is sufficiently general to include systems with an infinite number of degrees-of-freedom, including quantum fields. We show that a large number of states in relativistic quantum field theory, including the vacuum state and thermal equilibrium states, are distillable over subsystems separated by arbitrary spacelike distances. These results apply to any quantum field model. It will also be shown that these results can be generalized to quantum fields in curved spacetime, leading to the conclusion that there is a large number of quantum field states which are distillable over subsystems separated by an event horizon.

RELATIVISTIC PARTICLES WITH FRACTIONAL SPIN AND STATISTICS

1992 ◽  
Vol 07 (05) ◽  
pp. 1025-1057 ◽  
Author(s):  
STEFANO FORTE
Keyword(s):  
Path Integral ◽  
Degrees Of Freedom ◽  
Relativistic Quantum ◽  
Relativistic Quantum Mechanics ◽  
Integral Approach ◽  
Knot Invariants ◽  
Fractional Spin ◽  
Relativistic Particles ◽  
Spin And Statistics ◽  
Topological Term

We develop the relativistic quantum mechanics of particles with fractional spin and statistics in 2 + 1 dimensions in the path-integral approach. We endow the elementary excitations of the theory with fractional spin through the coupling of the particle number current with a topological term. We work out the dynamics of the spin degrees of freedom, and display the relation between the spin action and the knot invariants of the paths contributing to the path integral. We show that the explicit spin-changing interaction can be traded for multivaluedness of the wave function, and we relate this to the representation theory of the Lorentz and Poincaré groups in 2 + 1 dimensions. We discuss the multiparticle dynamics and derive the spin–statistics theorem.

Relativistic Multiple Scattering Theory

1991 ◽  
Vol 253 ◽  
Author(s):  
B. L. Gyorffy
Keyword(s):  
Quantum Mechanics ◽  
Degrees Of Freedom ◽  
Relativistic Quantum ◽  
Schr6dinger Equation ◽  
Relativistic Effects ◽  
Relativistic Quantum Mechanics ◽  
Absolute Minimum ◽  
Crystalline Anisotropy ◽  
Symmetry Properties ◽  
Finite Set

The symmetry properties of the Dirac equation, which describes electrons in relativistic quantum mechanics, is rather different from that of the corresponding Schr6dinger equation. Consequently, even when the velocity of light, c, is much larger than the velocity of an electron Vk, with wave vector, k, relativistic effects may be important. For instance, while the exchange interaction is isotropic in non-relativistic quantum mechanics the coupling between spin and orbital degrees of freedom in relativistic quantum mechanics implies that the band structure of a spin polarized metal depends on the orientation of its magnetization with respect to the crystal axis. As a consequence there is a finite set of degenerate directions for which the total energy of the electrons is an absolute minimum. Evidently, the above effect is the principle mechanism of the magneto crystalline anisotropy [1]. The following session will focus on this and other qualitatively new relativistic effects, such as dichroism at x-ray frequencies [2] or Fano effects in photo-emission from non-polarized solids [3].

scholarly journals PATH INTEGRATION IN RELATIVISTIC QUANTUM MECHANICS

1993 ◽  
Vol 08 (09) ◽  
pp. 1629-1635 ◽  
Author(s):  
IAN H. REDMOUNT ◽  
WAI-MO SUEN
Keyword(s):  
Path Integral ◽  
Light Cone ◽  
Proper Time ◽  
Relativistic Quantum ◽  
Free Particle ◽  
Wkb Approximation ◽  
Relativistic Quantum Mechanics ◽  
Path Integral Formulation ◽  
Quantum Theories ◽  
Short Time

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 a particle described by the simple relativistic action proportional to its proper time. This propagator is nonvanishing outside the light cone, implying that spacelike trajectories must be included in the path integral. The propagator matches the WKB approximation to the corresponding configuration-space path integral far from the light cone; outside the light cone that approximation consists of the contribution from a single spacelike geodesic. This propagator also has the unusual property that its short-time limit does not coincide with the WKB approximation, making the construction of a concrete skeletonized version of the path integral more complicated than in nonrelativistic theory.

Relativistic Quantum Fields

1966 ◽  
Vol 34 (4) ◽  
pp. 367-367 ◽  
Author(s):  
J. D. Bjorken ◽  
S. D. Drell ◽  
Peter B. Kahn
Keyword(s):  
Relativistic Quantum ◽  
Quantum Fields

Path Integral Methods for the Probabilistic Analysis of Nonlinear Systems Under a White-Noise Process

2020 ◽  
Vol 6 (4) ◽  
Author(s):  
Mario Di Paola ◽  
Gioacchino Alotta
Keyword(s):  
Path Integral ◽  
Path Integration ◽  
Integral Method ◽  
Degrees Of Freedom ◽  
Kolmogorov Equation ◽  
Integral Methods ◽  
Alternative Approach ◽  
Path Integration Method ◽  
Path Integral Method ◽  
Barrier Problems

Abstract In this paper, the widely known path integral method, derived from the application of the Chapman–Kolmogorov equation, is described in details and discussed with reference to the main results available in literature in several decades of contributions. The most simple application of the method is related to the solution of Fokker–Planck type equations. In this paper, the solution in the presence of normal, α-stable, and Poissonian white noises is first discussed. Then, application to barrier problems, such as first passage problems and vibroimpact problems is described. Further, the extension of the path integral method to problems involving multi-degrees-of-freedom systems is analyzed. Lastly, an alternative approach to the path integration method, that is the Wiener Path integration (WPI), also based on the Chapman–Komogorov equation, is discussed. The main advantages and the drawbacks in using these two methods are deeply analyzed and the main results available in literature are highlighted.

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