Related papers: Constructing Quantum Soliton States Despite Zero M…
The field theory Galilean symmetry, which was introduced in the context of modified gravity, gives a neat way to construct Lorentz-covariant theories of a scalar field, such that the equations of motion contain at most second-order…
The spectra of $A_r$ affine Toda field theories with imaginary coupling constant, are investigated. Soliton solutions are found, which, despite the non-unitary form of the Lagrangian, have real classical masses and are stable to small…
Noncommutative field theories with commutator of the coordinates of the form $[x^{\mu},x^{\nu}]=i \Lambda_{\quad \omega}^{\mu \nu}x^{\omega}$ are studied. Explicit Lorentz invariance is mantained considering $\Lambda $ a Lorentz tensor. It…
We consider the role of Lorentz symmetry in noncommutative field theory. We find that a Lorentz-violating standard-model extension involving ordinary fields is general enough to include any realisitc noncommutative field theory as a subset.…
Noncommutative solitons are easier to find in a noncommutative field theory. Similarly, the one-loop quantum corrections to the mass of a noncommutative soliton are easier to compute, in a real scalar theory in 2+1 dimensions. We carry out…
We study a soliton in an optical lattice holding bosonic atoms quantum mechanically using both an exact numerical solution and quantum Monte Carlo simulations. The computation of the state is combined with an explicit account of the…
It is well known that a theory with explicit Lorentz violation is not invariant under diffeomorphisms. On the other hand, for geometrical theories of gravity, there are alternative transformations, which can be best defined within the…
A structural explanation of the coupling constants in the standard model, i.e the fine structure constant and the Weinberg angle, and of the gauge fixing contributions is given in terms of symmetries and representation theory. The coupling…
We analyze the quantum dynamics of a relativistic homogeneous superfluid in a complex scalar field theory. Unlike zero-charge condensates, which undergo quantum evaporation due to internal number-changing processes, we show that $U(1)$…
The relation between symmetry reduction before and after quantization of a field theory is discussed using a toy model: the axisymmetric Klein-Gordon field. We consider three possible notions of symmetry at the quantum level: invariance…
We consider the translationally invariant Pauli-Fierz model describing a charged particle interacting with the electromagnetic field. We show under natural assumptions that the fiber Hamiltonian at zero momentum has a ground state.
Two series of integrable theories are constructed which have soliton solutions and can be thought of as generalizations of the sine-Gordon theory. They exhibit internal symmetries and can be described as gauged WZW theories with a potential…
Contrary to the common understanding, the Sine-Gordon equation in (1+2) dimensions does have N-soliton solutions for any N. The Hirota algorithm allows for the construction of static N-soliton solutions (i.e., solutions that do not depend…
Perturbative expansions of relativistic quantum field theories typically contain ultraviolet divergences requiring regularization and renormalization. Many different regularization techniques have been developed over the years, but most…
We find that, in presence of the Snyder geometry, the notion of translational invariance needs to be modified, allowing a momentum dependence of this symmetry. This step is necessary to build the maximally localized states and the Feynman…
Solitons in classical field theories correspond to states in quantum field theories. If the spatial dimension is infinite, then momentum eigenstates are not normalizable. This leads to infrared divergences, which are generally regularized…
In spite of its problems with interactions, the first-quantized Klein-Gordon equation is a satisfactory theory of free spinless particles. Moreover, the usual theory may be extended to describe Lorentz-violating behavior, of the same types…
Solid-like behavior at low energies and long distances is usually associated with the spontaneous breaking of spatial translations at microscopic scales, as in the case of a lattice of atoms. We exhibit three quantum field theories that are…
We show that a quantum state in a lattice spin (boson) system must be long-range entangled if it has non-zero lattice momentum, i.e. if it is an eigenstate of the translation symmetry with eigenvalue $e^{iP}\neq1$. Equivalently, any state…
Implications of noncommutative field theories with commutator of the coordinates of the form $[x^{\mu},x^{\nu}]=i \Lambda_{\quad \omega}^{\mu \nu}x^{\omega}$with nilpotent structure constants are investigated. It is shown that a free…