250 research outputs found
Building up spacetime with quantum entanglement
In this essay, we argue that the emergence of classically connected
spacetimes is intimately related to the quantum entanglement of degrees of
freedom in a non-perturbative description of quantum gravity. Disentangling the
degrees of freedom associated with two regions of spacetime results in these
regions pulling apart and pinching off from each other in a way that can be
quantified by standard measures of entanglement.Comment: Gravity Research Foundation essay, 7 pages, LaTeX, 5 figure
Quantization with maximally degenerate Poisson brackets: The harmonic oscillator!
Nambu's construction of multi-linear brackets for super-integrable systems
can be thought of as degenerate Poisson brackets with a maximal set of Casimirs
in their kernel. By introducing privileged coordinates in phase space these
degenerate Poisson brackets are brought to the form of Heisenberg's equations.
We propose a definition for constructing quantum operators for classical
functions which enables us to turn the maximally degenerate Poisson brackets
into operators. They pose a set of eigenvalue problems for a new state vector.
The requirement of the single valuedness of this eigenfunction leads to
quantization. The example of the harmonic oscillator is used to illustrate this
general procedure for quantizing a class of maximally super-integrable systems
Comment on "Feynman Effective Classical Potential in the Schrodinger Formulation"
We comment on the paper "Feynman Effective Classical Potential in the
Schrodinger Formulation"[Phys. Rev. Lett. 81, 3303 (1998)]. We show that the
results in this paper about the time evolution of a wave packet in a double
well potential can be properly explained by resorting to a variational
principle for the effective action. A way to improve on these results is also
discussed.Comment: 1 page, 2eps figures, Revte
Consistent two--dimensional chiral gravity
We study chiral induced gravity in the light-cone gauge and show that the
theory is consistent for a particular choice of chiralities. The corresponding
Kac--Moody central charge has no forbidden region of complex values.
Generalized analysis of the critical exponents is given and their relation to
the vacuum states is elucidated. All the parameters containing
information about the theory can be traced back to the characteristics of the
group of residual symmetry in the light--cone gauge.Comment: 38 pages, LateX, to appear in Int.J.Mod.Phys.
Classical and Quantum Nambu Mechanics
The classical and quantum features of Nambu mechanics are analyzed and
fundamental issues are resolved. The classical theory is reviewed and developed
utilizing varied examples. The quantum theory is discussed in a parallel
presentation, and illustrated with detailed specific cases. Quantization is
carried out with standard Hilbert space methods. With the proper physical
interpretation, obtained by allowing for different time scales on different
invariant sectors of a theory, the resulting non-Abelian approach to quantum
Nambu mechanics is shown to be fully consistent.Comment: 44 pages, 1 figure, 1 table Minor changes to conform to journal
versio
Dual theories for mixed symmetry fields. Spin-two case: (1,1) versus (2,1) Young symmetry type fields
We show that the parent Lagrangian method gives a natural generalization of
the dual theories concept for non p-form fields. Using this generalization we
construct here a three-parameter family of Lagrangians that are dual to the
Fierz-Pauli description of a free massive spin-two system. The dual field is a
three-index tensor T, which dinamically belongs to the (2,1) representation of
the Lorentz group. As expected, the massless limit of our Lagrangian, which is
parameter independent, has two propagating degrees of freedom per space point.Comment: 10 pages, no figure
Entanglement via Barut-Girardello coherent state for quantum algebra: bipartite composite system
Using noncocommutative coproduct properties of the quantum algebras, we
introduce and obtain, in a bipartite composite system, the Barut-Girardello
coherent state for the q-deformed algebra. The quantum coproduct
structure ensures this normalizable coherent state to be entangled. The
entanglement disappears in the classical limit, giving rise to a
factorizable state.Comment: 12 page
Implications of invariance of the Hamiltonian under canonical transformations in phase space
We observe that, within the effective generating function formalism for the
implementation of canonical transformations within wave mechanics, non-trivial
canonical transformations which leave invariant the form of the Hamilton
function of the classical analogue of a quantum system manifest themselves in
an integral equation for its stationary state eigenfunctions. We restrict
ourselves to that subclass of these dynamical symmetries for which the
corresponding effective generating functions are necessaarily free of quantum
corrections. We demonstrate that infinite families of such transformations
exist for a variety of familiar conservative systems of one degree of freedom.
We show how the geometry of the canonical transformations and the symmetry of
the effective generating function can be exploited to pin down the precise form
of the integral equations for stationary state eigenfunctions. We recover
several integral equations found in the literature on standard special
functions of mathematical physics. We end with a brief discussion (relevant to
string theory) of the generalization to scalar field theories in 1+1
dimensions.Comment: REVTeX v3.1, 13 page
Features of Time-independent Wigner Functions
The Wigner phase-space distribution function provides the basis for Moyal's
deformation quantization alternative to the more conventional Hilbert space and
path integral quantizations. General features of time-independent Wigner
functions are explored here, including the functional ("star") eigenvalue
equations they satisfy; their projective orthogonality spectral properties;
their Darboux ("supersymmetric") isospectral potential recursions; and their
canonical transformations. These features are illustrated explicitly through
simple solvable potentials: the harmonic oscillator, the linear potential, the
Poeschl-Teller potential, and the Liouville potential.Comment: 18 pages, plain LaTex, References supplemente
Can a strongly interacting Higgs boson rescue SU(5)?
Renormalization group analyses show that the three running gauge coupling
constants of the Standard Model do not become equal at any energy scale. These
analyses have not included any effects of the Higgs boson's self-interaction.
In this paper, I examine whether these effects can modify this conclusion.Comment: 8 pages (plus 4 postscript figures
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