A general approach to description of multigravity models in D-dimensional space-time is presented. Different possibilities of generalization of the invariant volume are given. Then a most general form of the interaction potential is constructed, which for bigravity coincides with the Pauli-Fierz model. A thorough analysis of the model along the 3+1 expansion formalism is done. It is shown that the absence of ghosts the considered bigravity model is equivalent in the weak field limit to the massive gravity (the Pauli-Fierz model). Thus, on the concrete example it is shown, that the interaction between metrics leads to nonvanishing mass of graviton.
Generalized structure of the interaction term of multigravity is analyzed in detail. The coincidence limit of any multigravity theory is defined and the compatibility equation for the interaction potential is derived which is studied in the weak perturbation limit of metric. The most general properties of the invariant volume and the scalar potential of multigravity are investigated. The general formula for multigravity invariant volume using three means (arithmetic, geometric and harmonic) is derived. The Pauli-Fierz mass term for bigravity in the weak field limit is obtained.
A new noncommutative spacetime of structure $ {\cal M}^4 \times Z_2 \times Z_2$ is proposed. The generalized Hilbert-Einstein action contains gravity, all known interactions and Higgs field. This theory can also provide a unified geometric framework for multigravity, which might explain the existence of dark matter and inflationary cosmology. In other words, high energy physics has laid out the crude shape of the new spacetime, while cosmology will shed light to the more details of it.
We confirm the stability of Podolsky's generalized electrodynamics by constructing a series of two-parametric bounded conserved quantities which includes the canonical energy-momentum tensors. In addition, we evaluate the transition-amplitude of this higher derivative system in BV antifield formalism and obtain the desirable generalized radiation gauge condition by choosing appropriate gauge-fixing fermion. Within the framework of Lagrangian BRST cohomology, we present the constructions of consistent interactions in Podolsky's model and when concentrating on the antighost number zero part of t…
Tensor models are natural generalizations of matrix models. The interactions and observables in the case of unitary invariant models are generalizations of matrix traces. Some notable interactions in the literature include the melonic ones, the tetrahedral one as well as the planar ones in rank three, or necklaces in even ranks. Here we introduce generalized melonic interactions which generalize the melonic and necklace interactions. We characterize them as tree-like gluings of quartic interactions. We also completely characterize the Feynman graphs which contribute to the large $N$ limit. For…
We study generalized Dirac oscillators with complex interactions in $(1+1)$ dimensions. It is shown that for the choice of interactions considered here, the Dirac Hamiltonians are $η$ pseudo Hermitian with respect to certain metric operators $η$. Exact solutions of the generalized Dirac Oscillator for some choices of the interactions have also been obtained. It is also shown that generalized Dirac oscillators can be identified with Anti Jaynes Cummings type model and by spin flip it can also be identified with Jaynes Cummings type model.
We derive a universal form for the correlation function of general n component systems in the limit of high temperatures or weak coupling. This enables the extraction of effective microscopic interactions from measured high temperature correlation functions. We find that in systems with long range interactions, there exist diverging correlation lengths with amplitudes that tend to zero in the high temperature limit. For general systems with disparate long range interactions, we introduce the notion of generalized Debye length (and time) scales and further relate it to the divergence of the lar…
We study the quantum corrections to the generalized Proca theory via matter loops. We consider two types of interactions, linear and nonlinear in the vector field. Calculating the one-loop correction to the vector field propagator, three- and four-point functions, we show that the non-linear interactions are harmless, although they renormalize the theory. The linear matter-vector field interactions introduce ghost degrees of freedom to the generalized Proca theory. Treating the theory as an effective theory, we calculate the energy scale up to which the theory remains healthy.
We extend previous results on healthy derivative self-interactions for a Proca field to the case of a set of massive vector fields. We obtain non-gauge invariant derivative self-interactions for the vector fields that maintain the appropriate number of propagating degrees of freedom. In view of the potential cosmological applications, we restrict to interactions with an internal rotational symmetry. We provide a systematical construction order by order in derivatives of the fields and making use of the antisymmetric Levi-Civita tensor. We then compare with the one single vector field case and …
In the search for an explanation for the current acceleration of the Universe, scalar fields are the most simple and useful tools to build models of dark energy. This field, however, must in principle couple with the rest of the world and not necessarily in the same way to different particles or fluids. We provide the most complete dynamical system analysis to date, consisting of a canonical scalar field conformally and disformally coupled to both dust and radiation. We perform a detailed study of the existence and stability conditions of the systems and comment on constraints imposed on the d…
We calculate the Casimir energy for scalar fields in interaction with finite-width mirrors, described by nonlocal interaction terms. These terms, which include quantum effects due to the matter fields inside the mirrors, are approximated by means of a local expansion procedure. As a result of this expansion, an effective theory for the vacuum field emerges, which can be written in terms of generalized $δ$-potentials. We compute explicitly the Casimir energy for these potentials and show that, for some particular cases, it is possible to reinterpret them as imposing imperfect Dirichlet boundary…
The interactions which preserve the structure of the gauge interactions of the free theory are introduced in terms of the generalized fields method of solving the Batalin-Vilkovisky master equation. It is shown that by virtue of this method the solution of the descent equations resulting from the cohomological analysis is provided straightforwardly. The general scheme is illustrated by applying it to spin-1 gauge field in 3 and 4 dimensions, to free BF theory in 2-d and to the antisymmetric tensor field in any dimension. It is shown that it reproduces the results obtained by cohomological tech…
We review the fundamentals of Jahn-Teller interactions and their field theoretical modelings and show that a 2+1 dimensional gauge theory where the gauge field couples to "flavored fermions" arises in a natural way from a two-band model describing the dynamical Jahn-Teller effect. The theory exhibits a second order phase transition to novel finite-temperature superconductivity.
We analyze the BRST field-antifield construction for generalized gauge fields consisting of massless mixed representations of the Lorentz Group and we calculate all the strictly gauge invariant interactions between them. All these interactions are higher derivative terms constructed out from the derivatives of the curl of field strength.
We investigate the impact of operators of higher canonical dimension on the lower Higgs mass consistency bound by means of generalized Higgs-Yukawa interactions. Analogously to higher-order operators in the bare Higgs potential in an effective field theory approach, the inclusion of higher-order Yukawa interactions, e.g., $ϕ^3\barψψ$, leads to a diminishing of the lower Higgs mass bound and thus to a shift of the scale of new physics towards larger scales by a few orders of magnitude without introducing a metastability in the effective Higgs potential. We observe that similar renormalization g…
For a (2+1)-dimensional Born-Infeld theory coupled to a recently proposed generalized connection, we compute the interaction potential within the structure of the gauge-invariant but path-dependent variables formalism. The result is equivalent to that of $QED_3$ with a Thirring interaction term among fermions, in the short distance regime. This result agrees with that of the topologically massive Born-Infeld theory.
We consider a generalization of nonrelativistic Schrödinger-Higgs Lagrangian by introducing a nonstandard kinetic term. We show that this model is Galilean invariant, we construct the conserved charges associated to the symmetries and realize the algebra of the Galilean group. In addition, we study the model in the presence of a gauge field. We also show that the gauged model is Galilean invariant. Finally, we explore relations between twin models and their solutions.
Self-dual vortex solutions are studied in detail in the generalized abelian Higgs model with independent Chern-Simons interaction. For special choices of couplings, it reduces to a Maxwell-Higgs model with two scalar fields, a Chern-Simons-Higgs model with two scalar fields, or other new models. We investigate the properties of the static solutions and perform detailed numerical analyses. For the Chern-Simons-Higgs model with two scalar fields in an asymmetric phase, we prove the existence of multisoliton solutions which can be viewed as hybrids of Chern-Simons vortices and $CP^1$ lumps. We al…
We construct a one-dimensional contact interaction ($ε$ potential) which induces the discontinuity of the wave function while keeping its derivative continuous. By combining the $ε$ potential and the Dirac's $δ$ function, we construct most general one-dimensional contact interactions allowable under the time reversal symmetry. We present some elementary results for the scattering problem which suggest a dual relation between $δ$ and $ε$ potentials.
We study $\mathbb{C}P^2$ Skyrmion crystals in the ferromagnetic SU(3) Heisenberg model with a generalization of the Dzyaloshinskii-Moriya interaction and the Zeeman term. The model possesses two different types of Skyrmion crystals with unit-Skyrmions that can be interpreted as bound states of two half-Skyrmions or four quarter-Skyrmions. Our study on $\mathbb{C}P^2$ Skyrmion crystals opens up the possibility for useful future applications since $\mathbb{C}P^2$ Skyrmions have more degrees of freedom than the usual $\mathbb{C}P^1$ (magnetic) Skyrmions.
The higher spin interaction currents for the conformally coupled scalar in $AdS_{4}$ space for both regular and irregular boundary condition corresponding to the free and interacting critical point of the boundary O(N) sigma model are constructed. The explicit form of the linearized interaction of the scalar and spin two and four gauge fields in the $AdS_{D}$ space using Noether's procedure for the corresponding spin two and four linearized gauge and generalized Weyl transformations are obtained.
