arXiv subjects

Silvester G. A. Borsboom

Publications and source records attributed to Silvester G. A. Borsboom.

5 recordsLinked to original sources

arXiv2026

Black hole equations of state and response functions

We systematically develop a framework for equilibrium thermodynamics in terms of thermodynamic representations, which are choices of thermodynamic potential and independent variables, one from each conjugate pair. In each representation, equations of state arise from first derivatives of the potential and response functions from its second derivatives. We apply this framework to ideal gases and to Schwarzschild black holes in a spherical cavity in various representations, interpreting the cavity area and its conjugate surface pressure as the thermodynamic volume and pressure of a holographically dual system. For this quasi-local Schwarzschild black hole, stability depends on the thermodynamic representation, or equivalently on which variables are held fixed under equilibrium perturbations. The large black hole branch is thermally stable at fixed volume but mechanically unstable under isothermal compression, while the system is mechanically stable under adiabatic compression everywhere. At fixed pressure, the black hole is thermally unstable throughout the physical state space. We also find that the thermal expansion coefficient is negative everywhere and show that isenthalpic expansion always cools the black hole. More broadly, the framework provides a systematic route to deriving equations of state and response functions for a wide class of black hole systems using quasi-local gravitational thermodynamics.

hep-th↗

arXiv2026

Global Gauge Symmetries and Spatial Asymptotic Boundary Conditions in Yang-Mills Theory

In Yang-Mills theory on a Euclidean Cauchy surface, the physical gauge group is often taken to be $\mathcal{G}^I/\mathcal{G}^\infty_0$, where $\mathcal{G}^I$ consists of boundary-preserving gauge transformations asymptoting to a constant, and $\mathcal{G}^\infty_0$ consists of transformations generated by the Gauss law constraint. We rigorously derive this physical gauge group for both Abelian and non-Abelian theories. A key result is that restricting to $\mathcal{G}^I$ follows from the structure of the instantaneous state space on which the instantaneous Lagrangian is defined. We extend our analysis to Yang-Mills-Higgs theory, showing that boundary conditions and the physical gauge group differ between the unbroken and broken phases.

math-ph↗

arXiv2026

Global Gauge Symmetry Breaking in the Abelian Higgs Mechanism

This paper aims to resolve the incompatibility between two extant gauge-invariant accounts of the Abelian Higgs mechanism: the first account uses global gauge symmetry breaking, and the second eliminates spontaneous symmetry breaking entirely. We resolve this incompatibility by using the constrained Hamiltonian formalism in symplectic geometry. First we argue that, unlike their local counterparts, global gauge symmetries are physical in the presence of boundary conditions. The symmetry that is spontaneously broken by the Higgs mechanism is this global one. Second, we explain how the Coulomb gauge is the preferred gauge for a gauge-invariant account of the Abelian Higgs mechanism. Based on the existence of the physical global gauge symmetry, we resolve the incompatibility between the two accounts by arguing that the correct way to carry out the second method is to eliminate only the redundant gauge symmetries, i.e. those local gauge symmetries which are not global. We extend our analysis to quantum field theory, where we show that the Abelian Higgs mechanism can be understood as spontaneous global $U(1)$ symmetry breaking in the $C^*$-algebraic sense.

physics.hist-ph↗

arXiv2026

Boundaries in the Instantaneous Formulation of Field Theories

We study boundary conditions in GiMmsy's covariant and instantaneous formulations of classical field theories and show that the instantaneous state space in the presence of a constant Dirichlet boundary condition is a tangent bundle to the configuration space of fields satisfying said condition. We then study the instantaneous state space when only the velocity of the field is required to vanish at the boundary and show that this results in a sector structure, where each sector is a tangent bundle labeled by the configuration at the boundary. Taking the Legendre transform of this sectored state space yields a sectored phase space with leafwise canonical Poisson structures. We apply this to Yang-Mills theory with spatial boundary conditions and relate our results to flux superselection sectors. The sector-moving gauge transformations are not Hamiltonian because of the lack of a boundary momentum, prompting us to propose a novel definition of the asymptotic or boundary symmetry group as the quotient of the boundary-preserving Hamiltonian transformations by the trivial ones. The physical boundary symmetry group of electromagnetism is then shown to be a copy of the global gauge group even when all sectors are considered simultaneously. Conditions are discussed under which the same holds for non-Abelian Yang-Mills theory.

math-ph↗

arXiv2026

Symmetry Breaking through Superselection by Boundary Conditions

Spontaneous symmetry breaking (SSB) is central to modern physics but is conventionally defined only for infinite systems, raising challenges for its interpretation in finite, real-world setups. This paper argues that the key to resolving this issue lies in the underappreciated role of boundary conditions in quantum systems. Inspired by both the relational approach to symmetries and the physical mechanism behind symmetry breaking, we formulate a relational interpretation of SSB: a finite system exhibits SSB relative to a reference environment which can induce perturbations across the boundary. This eliminates the need for the thermodynamic limit, offering a more physical picture of SSB that emphasizes the observable consequences of the interactions that real-life systems inevitably have with their environment. We show how, in this relational interpretation, SSB for both lattice systems and (gauge) field theories should be understood as subtle, rather than spontaneous, symmetry breaking, still in contrast to explicit symmetry breaking. We also explain how algebraic definitions of SSB for infinite systems relate to the intuitive picture of SSB in finite systems and illustrate how asymptotic boundary conditions push the environment "to infinity". In this way, our relational interpretation of SSB provides a unified conceptual framework applicable to symmetry-breaking in systems of any size.

physics.hist-ph↗