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I argue against the widespread notion that manifest de Sitter invariance on the full de Sitter manifold is either useful or even attainable in gauge theories. Green's functions and propagators computed in a de Sitter invariant gauge are…
Theories with gauge-mediated supersymmetry breaking provide an interesting alternative to the scenario in which the soft terms of the low-energy fields are induced by gravity. These theories allow for a natural suppression of flavour…
We discuss the problem of gauge fixing for the partition function in generalized quantum (or trace) dynamics, deriving analogs of the De Witt-Faddeev-Popov procedure and of the BRST invariance familiar in the functional integral context.
We contextualize the improved gauge-unfixing (GU) formalism within a rather general prototypical second-class system, obtaining a corresponding first-class equivalent description enjoying gauge invariance which can be applied to several…
The theory of cosmological perturbations is a well elaborated field. To deal with the diffeomorphism invariance of general relativity one generally introduces combinations of the metric and matter perturbations which are gauge invariant up…
There are a number of approaches to testing General Relativity (GR) on linear scales using parameterized frameworks for modifying cosmological perturbation theory. It is sometimes assumed that the details of any given parameterization are…
The issue of the physical equivalence between the different coordinate system in Einstein theory is revised. Gauge fixing influences results of measurements and physics are different in two different coordinate system. Spacetime metric…
We consider the problem of covariant gauge-fixing in the most general setting of the field-antifield formalism, where the action W and the gauge-fixing part X enter symmetrically and both satisfy the Quantum Master Equation. Analogous to…
We propose a distinction between the physical and the mathematical parts of gauge field theories. The main problem we face is to uphold a strong and meaningful criterion of what is physical. We like to call it "Field's dilemma", referring…
We analyze approaches to the partial or complete unification of gauge symmetries in theories with dynamical symmetry breaking. Several types of models are considered, including those that (i) involve sufficient unification to quantize…
Comparison of the gauge-invariant formulation for $l=0,1$-mode perturbations on the Schwarzschild background spacetime proposed in [K.~Nakamura, Class. Quantum Grav. {\bf 38} (2021), 145010.] and a ``conventional complete gauge-fixing…
An outline of a proof of the decomposition of linear metric perturbations into gauge-invariant and gauge-variant parts on an arbitrary background spacetime which admits ADM decomposition is briefly discussed. We explicitly construct the…
A specific class of gauge theories is geometrically described in terms of fermions. In particular, it is shown how the geometrical frame presented naturally includes spontaneous symmetry breaking of Yang-Mills gauge theories without making…
We provide a mechanism of gauging a theory based on a particular way to embed a theory on a target space such that a nontrivial fibration is produced. A connection over a nontrivial fibration with monodromy provides a natural framework for…
Recent years have seen strong progress in quantum simulation of gauge-theory dynamics using ultracold-atom experiments. A principal challenge in these efforts is the certification of gauge invariance, which has recently been realized in…
We discuss the so called gauge invariant quantization of anomalous gauge field theory, originally due to Faddeev and Shatashvili. It is pointed out that the further non invariance of relevant path integral measures poses a problem when one…
Perturbation theory in geometric theories of gravitation is a gauge theory of symmetric tensors defined on a Lorentzian manifold (the background spacetime). The gauge freedom makes uniqueness problems in perturbation theory particularly…
We give an introductory account of the recently identified gauge invariance of the equilibrium statistical mechanics of classical many-body systems [J. M\"uller et al., Phys. Rev. Lett. Phys. Rev. Lett. 133, 217101 (2024)]. The gauge…
This paper is an extended version of the talk given at 19th Texas Symposium of Relativistic Astrophysics and Cosmology, Paris, 1998. It reviews of some recent work; mathematical details are skipped. It is well-known that a choice of gauge…
We discuss various proposals of separating a tensor field into pure-gauge and gauge-invariant components. Such tensor field decomposition is intimately related to the effort of identifying the real gravitational degrees of freedom out of…