共查询到20条相似文献,搜索用时 93 毫秒
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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 gauge supersymmetry transformations as well as worldline reparametrizations. The simpler case of a spinless particle is first reviewed and it is pointed out that a strictly canonical approach does not exist. This follows formally from the gauge invariance properties of the action and physically it corresponds to the fact that particles can travel backwards as well as forward in coordinate time. However, appropriate application of path integral techniques yields directly the proper time representation of the Feynman propagator. Next we extend the formalism to systems described by anticommuting variables. This problem presents some difficulty when the dimension of the phase space is odd, because the holomorphic representation does not exist. It is shown, however, that the usual connection between the evolution operator and the path integral still holds provided one indludes in the action the boundary term that makes the classical variational principle well defined. The path integral for the relativistic spinning particle is then evaluated and it is shown to lead directly to a representation for the Feynman propagator in terms of two proper times, one commuting, the other anticommuting, which appear in a symmetric manner. This representation is used to derive scattering amplitudes in an external field. In this step the anticommuting proper time is integrated away and the analysis is carried in terms of one (commuting) proper time only, just as in the spinless case. Finally, some properties of the quantum mechanics of the ghost particles that appear in the path integral for constrained systems are developed in an appendix. 相似文献
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Mark S. Swanson 《Foundations of Physics》2000,30(3):359-370
The relationship between the canonical operator and the path integral formulation of quantum electrodynamics is analyzed with a particular focus on the implementation of gauge constraints in the two approaches. The removal of gauge volumes in the path integral is shown to match with the presence of zero-norm ghost states associated with gauge transformations in the canonical operator approach. The path integrals for QED in both the Feynman and the temporal gauges are examined and several ways of implementing the gauge constraint integrations are demonstrated. The upshot is to show that both the Feynman and the temporal gauge path integrals are equivalent to the Coulomb gauge path integral, matching the results developed by Kurt Haller using the canonical formalism. In addition, the Faddeev–Popov form for the Feynman gauge and temporal gauge Lagrangian path integrals are derived from the Hamiltonian form of the path integral. 相似文献
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Erik Aurell 《Journal of statistical physics》2018,171(5):745-767
The operation of a quantum computer is considered as a general quantum operation on a mixed state on many qubits followed by a measurement. The general quantum operation is further represented as a Feynman–Vernon double path integral over the histories of the qubits and of an environment, and afterward tracing out the environment. The qubit histories are taken to be paths on the two-sphere \(S^2\) as in Klauder’s coherent-state path integral of spin, and the environment is assumed to consist of harmonic oscillators initially in thermal equilibrium, and linearly coupled to to qubit operators \(\hat{S}_z\). The environment can then be integrated out to give a Feynman–Vernon influence action coupling the forward and backward histories of the qubits. This representation allows to derive in a simple way estimates that the total error of operation of a quantum computer without error correction scales linearly with the number of qubits and the time of operation. It also allows to discuss Kitaev’s toric code interacting with an environment in the same manner. 相似文献
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Joseph Dito 《Letters in Mathematical Physics》1990,20(2):125-134
The star-quantization of the free scalar field is developed by introducing an integral representation of the normal star-product. A formal connection between the Feynman path integral in the holomorphic representation and the star-exponential is established for the interacting scalar fields. 相似文献
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We review the probabilistic representation of quantum mechanics within which states are described by the probability distribution rather than by the wavefunction and density matrix. Uncertainty relations have been obtained in the form of integral inequalities containing measurable optical tomograms of quantum states. Formulas for the transition probabilities and purity parameter have been derived in terms of the tomographic probability distributions. Inequalities for Shannon and Rényi entropies associated with quantum tomograms have been obtained. A scheme of the star product of tomograms has been developed. 相似文献
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The probability representation for quantum states of the universe in which the states are described by a fair probability
distribution instead of wave function (or density matrix) is developed to consider cosmological dynamics. The evolution of
the universe state is described by standard positive transition probability (tomographic transition probability) instead of
the complex transition probability amplitude (Feynman path integral) of the standard approach. The latter one is expressed
in terms of the tomographic transition probability. Examples of minisuperspaces in the framework of the suggested approach
are presented. Possibility of observational applications of the universe tomographs are discussed. 相似文献
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The two-mode quantum electromagnetic field in the vacuum squeezed state is considered in the tomographic-probability representation.
The symplectic, center-of-mass, and photon-number tomograms for the two-mode vacuum squeezed state are obtained explicitly.
The expressions for photon statistics of the squeezed light are reconsidered using the state tomograms, and some new integral
relations are found for one and multimode orthogonal polynomials. 相似文献
10.
Dalcio K. Dacol 《Waves in Random and Complex Media》1994,4(2):117-126
A time-domain progressive wave equation is derived from the usual linear acoustic wave equation, and it is shown that the solution to this new equation can be expressed as a Feynman path integral. This path integral representation is used to derive the time-dependent statistics of acoustic fields propagating through random media. 相似文献
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J. Patera 《Journal of statistical physics》1972,5(3):185-188
It is shown that a modification of the usual gauge transformations is essential to the path integral formulation of nonrelativistic quantum mechanics as a consequence of defining the locality condition as follows: The contribution from each path comes entirely from the points on the path. Arguments are based on the similarity between Wiener and Feynman functional (path) integrals. 相似文献
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Stanley Gudder 《Foundations of Physics》1990,20(11):1345-1363
We first define a class of processes which we call regular quantum Markov processes. We next prove some basic results concerning such processes. A method is given for constructing quantum Markov processes using transition amplitude kernels. Finally we show that the Feynman path integral formalism can be clarified by approximating it with a quantum stochastic process. 相似文献
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V. Janiš 《Czechoslovak Journal of Physics》1990,40(8):836-856
We present an operator quantization scheme on a continuous direct product of Hilbert spaces over a time interval as an extension of the quantization using Feynman path integrals. We define the continuous direct product as a Hilbert space with two principal bases: the Fock and the Feynman ones. The Fock basis, defined by a complete set of commuting operators at different times, serves for a definition of the operator calculus. The Feynman basis, simultaneously diagonalizing the complete set of commuting operators, leads to path integrals constructed without time slicing as a spectral representation of certain operator functions. The construction of quantum theory and the corresponding path integrals for the harmonic oscillator is demonstrated both in the configuration and phase spaces. The extension of the theory to coherent states and anticommuting variables is performed. 相似文献
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《Journal of Geometry and Physics》2001,39(3):233-252
Both, spin and statistics of a quantum system can be seen to arise from underlying (quantum) group symmetries. We show that the spin–statistics theorem is equivalent to a unification of these symmetries. Besides covering the Bose–Fermi case we classify the corresponding possibilities for anyonic spin and statistics. We incorporate the underlying extended concept of symmetry into quantum field theory in a generalised path integral formulation capable of handling general braid statistics. For bosons and fermions the different path integrals and Feynman rules naturally emerge without introducing Grassmann variables. We also consider the anyonic example of quons and obtain the path integral counterpart to the usual canonical approach. 相似文献
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Wataru Ichinose 《Communications in Mathematical Physics》1997,189(1):17-33
We study the formulation of the Feynman path integral through broken line paths in non-relativistic quantum mechanics. This
formulation is very familiar to us and well known to be useful. But its rigorous meaning is given little except for special
cases. In the present paper, using the ideas in the theory of difference methods and the theory of pseudo-differential operators,
we show rigorously for some class of potentials that this formulation is well defined and that this Feynman path integral
gives the probability amplitude, i.e., the solution of the Schr?dinger equation.
Received: 21 August 1996 / Accepted: 13 February 1997 相似文献
16.
Unified treatment of the bound states of the Schioberg and the Eckart potentials using Feynman path integral approach
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We obtain analytical expressions for the energy eigenvalues of both the Schioberg and Eckart potentials using an approximation of the centrifugal term.In order to determine the e-states solutions,we use the Feynman path integral approach to quantum mechanics.We show that by performing nonlinear space-time transformations in the radial path integral,we can derive a transformation formula that relates the original path integral to the Green function of a new quantum solvable system.The explicit expression of bound state energy is obtained and the associated eigenfunctions are given in terms of hypergeometric functions.We show that the Eckart potential can be derived from the Schioberg potential.The obtained results are compared to those produced by other methods and are found to be consistent. 相似文献
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A. S. Sachrajda C. Gould G. Kirczenow B. Johnson Y. Feng P. J. Kelly A. Delage 《Physica E: Low-dimensional Systems and Nanostructures》1998,1(1-4)
A tunable two-antidot device is studied in the cyclotron-trapping regime. Periodic quantum oscillations are found to be superimposed on the peaks reminiscent of those observed in antidot lattices. The results are compared to quantum and classical simulations and Feynman path integral analysis. Published by Elsevier Science B.V. 相似文献
18.
The Feynman path integral is constructed for systems whose configuration space is a discrete finite set. The construction is based on the operator formulation of quantum mechanics on a finite discrete space. We derive connections between operators and introduce the analogue of the*-multiplication for discrete symbols. 相似文献
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邓履壁 《Frontiers of Physics》2012,7(2):239-243
In this paper, we have presented and established a new theoretical formulation of photon optics based on photon path and Feynman path integral idea. We have used Feynman path integral approach to discuss Fraunhofer, Fresnel diffraction of single photon and entangled photon pairs by ultrasonic wave and obtained the following results: i) quantum state and probability distribution of single photon and entangled photon pairs by Fraunhofer and Fresnel ultrasonic diffraction, ii) oblique incidence Raman-Nath and Bragg diffraction conditions, iii) total correlation state and its probability distribution. Our calculation results are in agreement with the experiment results. Comparing one-photon and two-photon diffraction effects by ultrasonic waves, we have found that two-photon diffraction by ultrasonic waves is also a sub-wavelength diffraction. 相似文献