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Supergeometric Quantum Field Theories (SG-QFTs) are theories that go beyond the standard supersymmetric framework, since they allow for general scalar-fermion field transformations on the configuration space of a supermanifold, without…
A canonical formulation of effective equations describes quantum corrections by the back-reaction of moments on the dynamics of expectation values of a state. As a first step toward an extension to quantum-field theory, these methods are…
We consider the evolution of quantum fields on a classical background space-time, formulated in the language of differential geometry. Time evolution along the worldlines of observers is described by parallel transport operators in an…
In the context of Covariant Quantum Mechanics for a spin particle, we classify the ``quantum vector fields'', i.e. the projectable Hermitian vector fields of a complex bundle of complex dimension 2 over spacetime. Indeed, we prove that the…
We give a mathematical definition of dynamical evolution in quantum field theory, including evolution on space-like surfaces, and show its relationship with the axiomatic and perturbative approaches to QFT.
Geometries with horizons offer insights into relationships between general relativity and quantum physics. Quantum mechanics constrains relationships between kinematic parameters and the coordinates describing the dynamics. Example quantum…
In this introductory article a brief description of Quantum Field Theories (QFT) is presented with emphasis on the distinction between strongly and weakly coupled theories. A case is made for using numerical simulations to solve QCD, the…
In physics, every observation is made with respect to a frame of reference. Although reference frames are usually not considered as degrees of freedom, in all practical situations it is a physical system which constitutes a reference frame.…
A rigorous treatment of light-matter interactions typically requires an interacting quantum field theory. However, most applications of interest are handled using classical or semiclassical models, which are valid only when quantum-field…
We first note that, at least in perturbation theory, there is a well-defined (subject to regularization) Lorentzian definition of the quantum effective action in both flat and curved space including (perturbative) gravity. The advantage of…
We review the effective field theory (EFT) approach to gravitational dynamics. We focus on extended objects in long-wavelength backgrounds and gravitational wave emission from spinning binary systems. We conclude with an introduction to EFT…
We outline a field theory on a multifractal spacetime. The measure in the action is characterized by a varying Hausdorff dimension and logarithmic oscillations governed by a fundamental physical length. A fine hierarchy of length scales…
We discuss the concept of gauge-invariant fields for non-abelian gauge theories. Infinitesimal fluctuations around a given gauge field can be split into physical and gauge fluctuations. Starting from some reference field the gauge-invariant…
The $f(R)$ theory of gravity can be expressed as a scalar tensor theory with a scalar degree of freedom $\phi$. By a conformal transformation, the action and its Gibbons-York-Hawking boundary term are written in the Einstein frame and the…
The alternative dynamics of loop quantum cosmology is examined by the path integral formulation. We consider the spatially flat FRW models with a massless scalar field, where the alternative quantization inherit more features from full loop…
Fluctuation and dissipation dynamics is examined at all temperature ranges for the general case of a background time evolving scalar field coupled to heavy intermediate quantum fields which in turn are coupled to light quantum fields. The…
The first part of this work deals with the development of a natural differential calculus on non-commutative manifolds. The second part extends the covariance and equivalence principle as well studies its kinematical consequences such as…
It is shown that, when there is a magnetic field present, in the framework of classical or quantum mechanics, the active translations differ from the passive ones and that the canonical momentum is not the generator of them. It is also…
We develop the idea that renormalization, decoupling of heavy particle effects from low energy physics and the construction of effective field theories are intimately linked to the momentum space entanglement of disparate modes of an…
Quintessence theories for cosmic acceleration imbue dark energy with a non-trivial dynamics that offers hope in distinguishing the physical origin of the component. We review quintessence models with an emphasis on this dynamics and discuss…