Poincaré invariance for continuous-time histories

Savvidou, Ntina

doi:10.1063/1.1471924

Cited by 31 publications

(70 citation statements)

References 12 publications

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“…This was developed by Griffiths [8], Omnés [9], Gell-Mann and Hartle [10,11]. This work is motivated from its elegant formulation that has been developed by Isham [12,13,14] and Savvidou [15,16].…”

Section: Consistent Historiesmentioning

confidence: 99%

“…This has been pointed out by Savvidou [15] and forms one of the basic features of the histories quantisation programme. We can define a purely kinematical time translation, by which the time translation is effected as 16) and there exists the dynamical time-translation generated by the Hamiltonian. These are completely distinct and correspond to the different functions of the notion of time in the physical theory (causal ordering/kinematics vs change/ dynamics).…”

Section: Quantum Differential Equationsmentioning

confidence: 99%

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Anastopoulos

2003

International Journal of Theoretical Physics

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We argue that the complex numbers are an irreducible object of quantum probability: this can be seen in the measurements of geometric phases that have no classical probabilistic analogue. Having the complex phases as primitive ingredient implies that we need to accept non-additive probabilities. This has the desirable consequence of removing constraints of standard theorems about the possibility of describing quantum theory with commutative variables. Motivated by the formalism of consistent histories and keeping an analogy with the theory of stochastic processes, we develop a (statistical) theory of quantum processes: they are characterised by the introduction of a "density matrix" on phase space paths (it thus includes phase information) and fully reproduces quantum mechanical predictions. We can write quantum differential equations (in analogy to Langevin equation) that could be interpreted as referring to individual quantum systems. We describe the reconstruction theorem by which a quantum process can yield the standard Hilbert space structure if the Markov property is imposed. We discuss the relevance of our results for the interpretation of quantum theory (a sample space is possible if probabilities are non-additive) and quantum gravity (the Hilbert space arises here after the consideration of a background causal structure).

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Section: Consistent Historiesmentioning

confidence: 99%

Section: Quantum Differential Equationsmentioning

confidence: 99%

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Anastopoulos

2003

International Journal of Theoretical Physics

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“…The histories formalism has been applied to scalar field theory on flat [7] and curved [9,10] space-times, and in the following we discuss the extension of the classical theory to the case of vector fields. In particular we examine the massive vector field and the electromagnetic field from a histories perspective.…”

Section: Motivationmentioning

confidence: 99%

Classical history theory of vector fields

Noltingk

2002

Journal of Mathematical Physics

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We consider the extension of classical history theory to the massive vector field and electromagnetism. It is argued that the action of the two Poincare groups introduced by Savvidou suggests that the history fields should have five components. The extra degrees of freedom introduced to make the fields five-dimensional result in an extra pair of second class constraints in the case of the massive vector field, and in an extended gauge group in the case of electromagnetism. The total gauge transformations depend on two arbitrary parameters, and contain 'internal' and 'external' U (1) gauge transformations as sub-

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“…The crucial step in the identification of the temporal structure of the theory was the definition in [10] of the action operator S -a quantum analogue of the Hamilton-Jacobi functional [12], written as…”

Section: Hpo-temporal Structurementioning

confidence: 99%

“…First, the Lorentzian metric is quantised, as a direct analogue of the way the 'external' quantum field arises in the history approach to scalar quantum field theory [10,11]. On the other hand, in the conventional canonical quantum gravity schemes only the spatial metric on a three-surface is quantised.…”

Section: Introductionmentioning

confidence: 99%

General relativity histories theory

Savvidou¹

2005

Braz. J. Phys.

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The canonical description is based on the prior choice of a spacelike foliation, hence making a reference to a spacetime metric. However, the metric is expected to be a dynamical, fluctuating quantity in quantum gravity. After presenting the developments in the History Projection Operator histories theory in the last seven yearsgiving special emphasis on the novel temporal structure of the formalism -we show how this problem can be solved in the histories formulation of general relativity. We implement the 3 + 1 decomposition using metricdependent foliations which remain spacelike with respect to all possible Lorentzian metrics. This allows us to find an explicit relation of covariant and canonical quantities which preserves the spacetime character of the canonical description. In this new construction we have a coexistence of the spacetime diffeomorphisms group Diff(M) and the Dirac algebra of constraints.

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Poincaré invariance for continuous-time histories

Cited by 31 publications

References 12 publications

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Classical history theory of vector fields

General relativity histories theory

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