An Algebraic Approach to Physical Scales

Janyška, Josef; Modugno, Marco; Vitolo, Raffaele

doi:10.1007/s10440-009-9505-6

Cited by 29 publications

(28 citation statements)

References 25 publications

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“…1 In particular, the notion of 1-dimensional positive space captures the essential point about unit spaces, and tensor products between a unit space and a vector space allow us to handle spaces which are similar but differently scaled. We also stress that the ensuing formalism is quite handy, though the demonstrations of certain basic properties are not trivial [11].…”

Section: Unit Spacesmentioning

confidence: 98%

“…A point-like source is represented by a couple (x, v) ∈ M × V , and Ξ(x, x ′ )⌋v is the corresponding field produced by it. 11 The fact that i D ret η = ǫ + and i D adv η = −ǫ − are elementary solutions of the wave equation, namely ǫ ± = ±δ , can be calso checked by a direct calculation. See for example Choquet-Bruhat and DeWittMorette [9], § VI.C.5, page 511.…”

Section: Propagators and Vector-valued Fieldsmentioning

confidence: 99%

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Special generalized densities and propagators: A geometric account

Canarutto¹

2016

Int. J. Geom. Methods Mod. Phys.

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Starting from a short review of spaces of generalized sections of vector bundles, we give a concise systematic description, in precise geometric terms, of Leray densities, principal value densities, propagators and elementary solutions of field equations in flat spacetime. We then sketch a partly original geometric presentation of free quantum fields and show how propagators arise from their graded commutators in the boson and fermion cases.2010 MSC: 46F12, 35R99, 81T05.

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Section: Unit Spacesmentioning

confidence: 98%

Section: Propagators and Vector-valued Fieldsmentioning

confidence: 99%

Special generalized densities and propagators: A geometric account

Canarutto¹

2016

Int. J. Geom. Methods Mod. Phys.

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“…These points can be conveniently expressed in terms of components, as we are going to do after introducing some further notational details. 4 A convenient, general setting for the treatment of physical units (see [23,8] for details) was introduced after an idea by M. Modugno and then adopted by several authors. The consistent use of that approach is indeed a source of mathematical clarity, and as such it is used here (it is not specially needed for higher-spin fields).…”

Section: Two-spinors and Dirac Spinorsmentioning

confidence: 99%

A first-order Lagrangian theory of fields with arbitrary spin

Canarutto¹

2018

Int. J. Geom. Methods Mod. Phys.

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The bundles suitable for a description of higher-spin fields can be built in terms of a 2-spinor bundle as the basic 'building block'. This allows a clear, direct view of geometric constructions aimed at a theory of such fields on a curved spacetime. In particular, one recovers the Bargmann-Wigner equations and the 2(2j + 1)-dimensional representation of the angular-momentum algebra needed for the Joos-Weinberg equations. Looking for a first-order Lagrangian field theory we argue, through considerations related to the 2-spinor description of the Dirac map, that the needed bundle must be a fibered direct sum of a symmetric 'main sector'-carrying an irreducible representation of the angularmomentum algebra-and an induced sequence of 'ghost sectors'. Then one indeed gets a Lagrangian field theory that, at least formally, can be expressed in a way similar to the Dirac theory. In flat spacetime one gets plane-wave solutions that are characterised by their values in the main sector. Besides symmetric spinors, the above procedures can be adapted to anti-symmetric spinors and to Hermitian spinors (the latter describing integer-spin fields). Through natural decompositions, the case of a spin-2 field describing a possible deformation of the spacetime metric can be treated in terms of the previous results.MSC 2010: 81R20, 81R25.

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“…Unit spaces. The theory of unit space has been developed in [20] in order to make explicit the independence of classical and quantum mechanics from the choice of unit of measurements. Unit spaces have the same algebraic structure as IR + , but no natural basis.…”

Section: Preliminariesmentioning

confidence: 99%

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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An Algebraic Approach to Physical Scales

Cited by 29 publications

References 25 publications

Special generalized densities and propagators: A geometric account

Special generalized densities and propagators: A geometric account

A first-order Lagrangian theory of fields with arbitrary spin

On the characterization of infinitesimal symmetries of the relativistic phase space

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