Covariant Quantum Mechanics and Quantum Symmetries

Janyška, Josef; Modugno, Marco; Saller, Dirk

doi:10.1007/978-88-470-2101-3_13

Cited by 7 publications

(3 citation statements)

References 16 publications

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“…In our approach to the phase space we obtain results which are "parallel" to results for Galilean spacetime in [19,26,32]. Namely, we prove that all projectable infinitesimal symmetries of the generalized contact structure are holonomic lifts to the phase space of infinitesimal symmetries of g and F .…”

Section: Introductionsupporting

confidence: 59%

“…In our approach to the phase space, we obtain results which are 'parallel' to results for Galilean spacetime in [19,26,32]. Namely we prove that all projectable infinitesimal symmetries of the generalized contact structure are holonomic lifts to the phase space of infinitesimal symmetries of g and F. Here, 'projectable' means that we consider infinitesimal symmetries that project onto vector fields on spacetime, and 'holonomic lift' means the lift of a vector field to the first jet space.…”

Section: Introductionsupporting

confidence: 52%

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On the characterization of infinitesimal symmetries of the relativistic phase space

Janyška

Vitolo²

2012

J. Phys. A: Math. Theor.

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The phase space of relativistic particle mechanics is defined as the 1st jet space of motions regarded as timelike 1-dimensional submanifolds of spacetime. A Lorentzian metric and an electromagnetic 2-form define naturally on the odd-dimensional phase space a generalized contact structure. In the paper infinitesimal symmetries of the phase structures are characterized. More precisely, it is proved that all phase infinitesimal symmetries are special Hamiltonian lifts of distinguished conserved quantities on the phase space. It is proved that generators of infinitesimal symmetries constitute a Lie algebra with respect to a special bracket. A momentum map for groups of symmetries of the geometric structures is provided.

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Section: Introductionsupporting

confidence: 59%

Section: Introductionsupporting

confidence: 52%

On the characterization of infinitesimal symmetries of the relativistic phase space

Janyška

Vitolo²

2012

J. Phys. A: Math. Theor.

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“…A covariant formulation of classical and quantum mechanics on a curved spacetime with absolute time based on fibred manifolds, jets, non linear connections, cosymplectic forms and Frölicher smooth spaces has been proposed by A. Jadczyk and M. Modugno [28,29] and further developed by several authors (see, for instance, [8,30,31,34,53,61,48]). We shall briefly call this approach "covariant quantum mechanics".…”

Section: Introductionmentioning

confidence: 99%

A covariant approach to the quantization of a rigid body

Modugno¹,

Prieto²,

Vitolo³

2008

J. Phys. A: Math. Theor.

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This paper concerns the quantisation of a rigid body in the framework of "covariant quantum mechanics" on a curved spacetime with absolute time.The basic idea is to consider the multi-configuration space, i.e. the configuration space for n particles, as the n-fold product of the configuration space for one particle. Then we impose a rigid constraint on the multi-configuration space. The resulting space is then dealt with as a configuration space of a single abstract 'particle'. The same idea is applied to all geometric and dynamical structures.We show that the above configuration space fits into the general framework of "covariant quantum mechanics". Hence, the methods of this theory can be applied to the rigid body.Accordingly, we find exactly two inequivalent choices of quantum structures for the rigid body. Then, we evaluate the quantum energy and momentum operators and the 'rotational part' of their spectra. We provide a new mathematical interpretation of two-valued wavefunctions on SO(3) in terms of single-valued sections of a new non-trivial quantum bundle. These results have clear analogies with spin.

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