A puzzle concerning local symmetries and their empirical significance

Assigning Values and States

10.1093/oso/9780198714057.003.0005 ◽

2017 ◽

Author(s):

Richard Healey

Keyword(s):

Quantum State ◽

Density Operator ◽

Entangled State ◽

Physical Situation ◽

Born Rule ◽

Correct Assignment ◽

Significant Magnitude ◽

Good Advice ◽

Empirical Significance ◽

Important Idea

If a quantum state is prescriptive then what state should an agent assign, what expectations does this justify, and what are the grounds for those expectations? I address these questions and introduce a third important idea—decoherence. A subsystem of a system assigned an entangled state may be assigned a mixed state represented by a density operator. Quantum state assignment is an objective matter, but the correct assignment must be relativized to the physical situation of an actual or hypothetical agent for whom its prescription offers good advice, since differently situated agents have access to different information. However this situation is described, it is true, empirically significant magnitude claims that make the description correct, while others provide the objective grounds for the agent’s expectations. Quantum models of environmental decoherence certify the empirical significance of these magnitude claims while also licensing application of the Born rule to others without mentioning measurement.

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Nilpotent symmetries as a mechanism for Grand Unification

Journal of High Energy Physics ◽

10.1007/jhep05(2021)240 ◽

2021 ◽

Vol 2021 (5) ◽

Author(s):

Lars Andersson ◽

András László ◽

Błażej Ruba

Keyword(s):

Gauge Field ◽

Scalar Product ◽

Local Symmetry ◽

Matter Field ◽

Gauge Fields ◽

Spacetime Symmetries ◽

Invariant Scalar ◽

Spacetime Manifold ◽

Local Symmetries ◽

Dilatation Group

Abstract In the classic Coleman-Mandula no-go theorem which prohibits the unification of internal and spacetime symmetries, the assumption of the existence of a positive definite invariant scalar product on the Lie algebra of the internal group is essential. If one instead allows the scalar product to be positive semi-definite, this opens new possibilities for unification of gauge and spacetime symmetries. It follows from theorems on the structure of Lie algebras, that in the case of unified symmetries, the degenerate directions of the positive semi-definite invariant scalar product have to correspond to local symmetries with nilpotent generators. In this paper we construct a workable minimal toy model making use of this mechanism: it admits unified local symmetries having a compact (U(1)) component, a Lorentz (SL(2, ℂ)) component, and a nilpotent component gluing these together. The construction is such that the full unified symmetry group acts locally and faithfully on the matter field sector, whereas the gauge fields which would correspond to the nilpotent generators can be transformed out from the theory, leaving gauge fields only with compact charges. It is shown that already the ordinary Dirac equation admits an extremely simple prototype example for the above gauge field elimination mechanism: it has a local symmetry with corresponding eliminable gauge field, related to the dilatation group. The outlined symmetry unification mechanism can be used to by-pass the Coleman-Mandula and related no-go theorems in a way that is fundamentally different from supersymmetry. In particular, the mechanism avoids invocation of super-coordinates or extra dimensions for the underlying spacetime manifold.

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On Galilean Invariant and Energy Preserving BBM-Type Equations

Symmetry ◽

10.3390/sym13050878 ◽

2021 ◽

Vol 13 (5) ◽

pp. 878

Author(s):

Alexei Cheviakov ◽

Denys Dutykh ◽

Aidar Assylbekuly

Keyword(s):

Wave Equation ◽

Conservation Laws ◽

Numerical Simulations ◽

Solitary Waves ◽

Local Symmetry ◽

Symmetry And Conservation Laws ◽

Higher Order ◽

Special Equation ◽

Long Wave ◽

Local Symmetries

We investigate a family of higher-order Benjamin–Bona–Mahony-type equations, which appeared in the course of study towards finding a Galilei-invariant, energy-preserving long wave equation. We perform local symmetry and conservation laws classification for this family of Partial Differential Equations (PDEs). The analysis reveals that this family includes a special equation which admits additional, higher-order local symmetries and conservation laws. We compute its solitary waves and simulate their collisions. The numerical simulations show that their collision is elastic, which is an indication of its S−integrability. This particular PDE turns out to be a rescaled version of the celebrated Camassa–Holm equation, which confirms its integrability.

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Constructing Carrollian CFTs

Journal of High Energy Physics ◽

10.1007/jhep03(2021)194 ◽

2021 ◽

Vol 2021 (3) ◽

Author(s):

Nishant Gupta ◽

Nemani V. Suryanarayana

Keyword(s):

Scalar Fields ◽

Higher Dimensions ◽

Field Theories ◽

Conformal Field Theories ◽

Relativistic Limit ◽

Conformal Field ◽

Local Symmetries ◽

Derivatives Of ◽

Special Case

Abstract We construct classical theories for scalar fields in arbitrary Carroll spacetimes that are invariant under Carrollian diffeomorphisms and Weyl transformations. When the local symmetries are gauge fixed these theories become Carrollian conformal field theories. We show that generically there are at least two types of such theories: one in which only time derivatives of the fields appear and the other in which both space and time derivatives appear. A classification of such scalar field theories in three (and higher) dimensions up to two derivative order is provided. We show that only a special case of our theories arises in the ultra-relativistic limit of a covariant parent theory.

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Accidental Gauge Symmetries of Minkowski Spacetime in Teleparallel Theories

Universe ◽

10.3390/universe7050143 ◽

2021 ◽

Vol 7 (5) ◽

pp. 143

Author(s):

Jose Beltrán Jiménez ◽

Tomi S. Koivisto

Keyword(s):

General Relativity ◽

Minkowski Spacetime ◽

Linear Extensions ◽

Gauge Symmetries ◽

Linear Spectrum ◽

Massless Spin ◽

Non Linear ◽

Common Framework ◽

Local Symmetries ◽

Quadratic Action

In this paper, we provide a general framework for the construction of the Einstein frame within non-linear extensions of the teleparallel equivalents of General Relativity. These include the metric teleparallel and the symmetric teleparallel, but also the general teleparallel theories. We write the actions in a form where we separate the Einstein–Hilbert term, the conformal mode due to the non-linear nature of the theories (which is analogous to the extra degree of freedom in f(R) theories), and the sector that manifestly shows the dynamics arising from the breaking of local symmetries. This frame is then used to study the theories around the Minkowski background, and we show how all the non-linear extensions share the same quadratic action around Minkowski. As a matter of fact, we find that the gauge symmetries that are lost by going to the non-linear generalisations of the teleparallel General Relativity equivalents arise as accidental symmetries in the linear theory around Minkowski. Remarkably, we also find that the conformal mode can be absorbed into a Weyl rescaling of the metric at this order and, consequently, it disappears from the linear spectrum so only the usual massless spin 2 perturbation propagates. These findings unify in a common framework the known fact that no additional modes propagate on Minkowski backgrounds, and we can trace it back to the existence of accidental gauge symmetries of such a background.

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