Related papers: Caustic Formation upon Shift Symmetry Breaking
This paper summarises a numerical investigation of how the usual manifestations of chaos and regularity for flows in time-independent Hamiltonians can be alterred by a systematic time-dependence of the form arising naturally in an expanding…
We present a clear and mathematically simple procedure explaining spontaneous symmetry breaking in quantum mechanical systems. The procedure is applicable to a wide range of models and can be easily used to explain the existence of a…
Some formal aspects of supersymmetry breaking are reviewed. The classic "requirements" for supersymmetry breaking include chiral matter, a dynamical superpotential, and a classical superpotential which completely lifts the moduli space.…
"Physical theories of fundamental significance tend to be gauge theories. These are theories in which the physical system being dealt with is described by more variables than there are physically independent degree of freedom. The…
The extraordinary success of the Standard Model asks for a more rigorous control beyond the perturbative approach, which is affected by mathematical problems (interaction picture and canonical quantization, non-convergence of the…
A canonical formalism and constraint analysis for discrete systems subject to a variational action principle are devised. The formalism is equivalent to the covariant formulation, encompasses global and local discrete time evolution moves…
We study some properties of the canonical transformations in classical mechanics and quantum field theory and give a number of practical formulas concerning their generating functions. First, we give a diagrammatic formula for the…
We show the absence of continuous symmetry breaking in 2D lattice systems without any smoothness assumptions on the interaction. We treat certain cases of interactions with integrable singularities. We also present cases of singular…
Supersymmetry breaking by the quantum deformation of a classical moduli space is considered. A simple, non-chiral, renormalizable model is presented to illustrate this mechanism. The well known, chiral, $SU(3) \times SU(2)$ model and its…
The Hamiltonian formulation plays the essential role in constructing the framework of modern physics. In this paper, a new form of canonical equations of Hamilton with the complete symmetry is obtained, which are valid not only for the…
Recently we have described a mechanical system which exhibits spontaneous breaking of Z_2 symmetry and related topological kinks called compactons. The corresponding field potential is not differentiable at its global minima. Therefore,…
We argue that there is nothing puzzling in the fact that the Hamiltonian formulation of a covariant theory, General Relativity, after a non-covariant change of field variables is not canonically related to the formulation based on the…
Explicit symmetry breaking occurs when a dynamical system having a certain symmetry group is perturbed in a way that the perturbation preserves only some symmetries of the original system. We give a geometric approach to study this…
If a unitary transformation has a decomposition into a quantum circuit with no directed path from input $a$ to output $b$, then $a$ does not influence $b$ through the overall unitary. Conversely, it is known that if $a$ does not influence…
Caustics occur widely in dynamics and take on shapes classified by catastrophe theory. At finite wavelengths they produce interference patterns containing networks of vortices (phase singularities). Here we investigate caustics in quantized…
The description of spontaneous symmetry breaking that underlies the connection between classically ordered objects in the thermodynamic limit and their individual quantum mechanical building blocks is one of the cornerstones of modern…
The trajectories of the pilot-wave formulation of quantum mechanics and hence its empirical predictions may be recovered via the dynamics of a density function on the configuration space of a system, without reference to a physical wave…
The scalar field is quantized in the discretized light-front framework following the {\em standard} Dirac procedure and its infinite volume limit taken. The background field and the nonzero mode variables do not commute for finite volume;…
Dynamics of ideal fluid with free surface can be effectively solved by perturbing the Hamiltonian in weak nonlinearity limit. However it is shown that perturbation theory, which includes third and fourth order terms in the Hamiltonian,…
Spontaneous symmetry breaking (SSB) is a widespread phenomenon in several areas of physics. In this paper I wish to illustrate some situations where spontaneous symmetry breaking presents non obvious aspects. The first example is taken from…