Coherent State Path Integral (original) (raw)
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Coherent-state path integrals in the continuum
Physical Review A, 2014
We discuss the time-continuous path integration in the coherent states basis in a way that is free from inconsistencies. Employing this notion we reproduce known and exact results working directly in the continuum. Such a formalism can set the basis to develop perturbative and non-perturbative approximations already known in the quantum field theory community. These techniques can be proven useful in a great variety of problems where bosonic Hamiltonians are used.
Breakdown of the coherent state path integral: two simple examples
Physical Review Letters, 2011
We show how the time-continuous coherent state path integral breaks down for both the single-site Bose-Hubbard model and the spin path integral. Specifically, when the Hamiltonian is quadratic in a generator of the algebra used to construct coherent states, the path integral fails to produce correct results following from an operator approach. As suggested by previous authors, we note that the problems do not arise in the time-discretized version of the path integral.
1997
Quantum mechanical phase space path integrals are re-examined with regard to the physical interpretation of the phase space variables involved. It is demonstrated that the traditional phase space path integral implies a meaning for the variables involved that is manifestly inconsistent. On the other hand, a phase space path integral based on coherent states entails variables that exhibit a self-consistent physical meaning.
Weak coherent state path integrals
Journal of Mathematical Physics, 2004
Weak coherent states share many properties of the usual coherent states, but do not admit a resolution of unity expressed in terms of a local integral. They arise e.g. in the case that a group acts on an inadmissible fiducial vector. Motivated by the recent Affine Quantum Gravity Program, the present article studies the path integral representation of the affine weak coherent state matrix elements of the unitary time-evolution operator. Since weak coherent states do not admit a resolution of unity, it is clear that the standard way of constructing a path integral, by time slicing, is predestined to fail. Instead a well-defined path integral with Wiener measure, based on a continuous-time regularization, is used to approach this problem. The dynamics is rigorously established for linear Hamiltonians, and the difficulties presented by more general Hamiltonians are addressed.
Coherent State Path Integrals without Resolutions of Unity
2000
From the very beginning, coherent state path integrals have always relied on a coherent state resolution of unity for their construction. By choosing an inadmissible fiducial vector, a set of ``coherent states'' spans the same space but loses its resolution of unity, and for that reason has been called a set of weak coherent states. Despite having no resolution of unity, it is nevertheless shown how the propagator in such a basis may admit a phase-space path integral representation in essentially the same form as if it had a resolution of unity. Our examples are toy models of similar situations that arise in current studies of quantum gravity.
Coherent State Path Integrals at (Nearly) 40
1998
Coherent states can be used for diverse applications in quantum physics including the construction of coherent state path integrals. Most definitions make use of a lattice regularization; however, recent definitions employ a continuous-time regularization that may involve a Wiener measure concentrated on continuous phase space paths. The introduction of constraints is both natural and economical in coherent state path integrals involving only the dynamical and Lagrange multiplier variables. A preliminary indication of how these procedures may possibly be applied to quantum gravity is briefly discussed.
On the role of coherent states in quantum foundations
Optics and Spectroscopy, 2011
Coherent states, and the Hilbert space representations they generate, provide ideal tools to discuss classical/quantum relationships. In this paper we analyze three separate classical/quantum problems using coherent states, and show that useful connections arise among them. The topics discussed are: (1) a truly natural formulation of phase space path integrals; (2) how this analysis implies that the usual classical formalism is "simply a subset" of the quantum formalism, and thus demonstrates a universal coexistence of both the classical and quantum formalisms; and (3) how these two insights lead to a complete analytic solution of a formerly insoluble family of nonlinear quantum field theory models.
Reply to “Comment on ‘Coherent-state path integrals in the continuum’”
Physical Review A, 2019
In this Reply we briefly clarify the main points of our method to construct coherent-state path integrals in the continuum and we reply to the critique raised by in the preceding Comment by Kochetov [Phys. Rev. A 99, 026101 (2019)]. By using definite examples, we prove that our approach is capable of resolving the inconsistencies accompanying the standard coherent-state path-integral representation of interacting systems.
Coherent-state path integrals in the continuum: The SU(2) case
Annals of Physics, 2016
We define the time-continuous spin coherent-state path integral in a way that is free from inconsistencies. The proposed definition is used to reproduce known exact results. Such a formalism opens new possibilities for applying approximations with improved accuracy and can be proven useful in a great variety of problems where spin Hamiltonians are used.
Extended coherent states and path integrals with auxiliary variables
Journal of Physics A: Mathematical …, 1993
The usual construction of mherent slates allows a wider interpretation in which the number of distinguishing slate labels is no longer minimal; the label measure determining the required m l u t i o n of unity is then no longer unique and may even be concentrated on manifolds with positive mdimension. Paying particular attention to the H ( E ) = ( e l w ) (2.6) the other, the lower symbol, is defined through the equation 71 = h(E)lE)(El6E J