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Franco Strocchi

Publications and source records attributed to Franco Strocchi.

13 recordsLinked to original sources
arXiv2024

Why Gauges? Gauge symmetries for the classification of the physical states

This note focuses the problem of motivating the use of gauge symmetries (being the identity on the observables) from general principles, beyond their practical success, starting from global gauge symmetries and then by emphasizing the substantially different role of local gauge symmetries. In the latter case, a deterministic time evolution of the local field algebra, necessary for field quantization, requires a reduction of the full local gauge group $\cal{G}$ to a residual local subgroup $\cal{G}_r$ satisfying suitable conditions. A non-trivial residual local gauge group allows for a description/construction of the physical states by using the vacuum representation of a local field algebra, otherwise precluded if $\cal{G}$ is reduced to the identity. Moreover, in the non-abelian case the non-trivial topology of the a residual $\cal{G}_r$ defines the (gauge invariant) topological invariants which classify the vacuum structure with important physical effects; furthermore, it provides a general mechanism of spontaneous symmetry breaking without Goldstone bosons.

physics.hist-ph↗
arXiv2023

A note on Gauss operators and quantizations of Yang-Mills theories

The quantization of Yang-Mills field theories requires the introduction of a gauge fixing which leads to a violation of the Local Gauss Law described by the so-called Gauss operator. We discuss the local quantizations of Yang-Mills theories in terms of the possible Gauss operators, which are argued to have a more physical meaning than the gauge fixings. We focus the attention on the local quantizations which leave the global gauge group and a subgroup of local gauge transformations unbroken, as the Feynman quantization of quantum Electrodynamics, and show that in the non-abelian case such properties cannot be realized together with Lorentz covariance; thus, quite generally, one cannot have the structural properties of the Feynman quantization of Quantum Electrodynamics. By relaxing the condition of Lorentz covariance, we obtain a classification of Gauss operators, which satisfy gauge covariant conservation laws and generate non-trivial residual subgroups of local gauge transformations.

hep-th↗
arXiv2023

Local Gauss law and local gauge symmetries in QFT

Local gauge symmetries reduce to the identity on the observables, as well as on the physical states (apart from reflexes of the local gauge group topology) and therefore their use in Quantum Field Theory (QFT) asks for a justification of their strategic role. They play an intermediate role in deriving the validity of Local Gauss Laws on the physical states (for the currents which generate the related global gauge group); conversely, we show that local gauge symmetries arise whenever a vacuum representation of a local field algebra ${\cal{F}}$ is used for the description/construction of physical states satisfying Local Gauss Laws, just as global compact gauge groups arise for the description of localizable states labeled by superselected quantum numbers. The above relation suggests that the Gauss operator, which by locality cannot vanish in ${\cal{F}}$, provides an intrinsic characterization of the realizations of a gauge QFT in terms of a local field algebra and of the related local gauge symmetries.

hep-th↗
arXiv2022

Some Rigorous Results on Symmetry Breakings in Gauge QFT

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 perturbative series, trivialy results for the $\ph^4$ model and related models etc.). We shall briefly discuss sone non-perturbative results concerning the crucial role and realization of symmetry breakings in the Standard Model.

hep-th↗
arXiv2020

Generalized criteria of symmetry breaking. A strategy for quantum time crystals

The aim of this paper is to propose a criterion of spontaneous symmetry breaking that makes reference to the properties of pure phases defined by a translationally invariant state. By avoiding any reference to the ground state, at the basis of the standard approach, this criterion applies to a wider class of models. An interesting application is the breaking of time translations. Indeed, we discuss explicit theoretical models which exhibit the prototypical features of quantum time crystals, without the need of a time-dependent Hamiltonian.

cond-mat.stat-mech↗
arXiv2020

Corrections to Wigner-Eckart Relations by Spontaneous Symmetry Breaking

The matrix elements of operators transforming as irreducible representations of an unbroken symmetry group $G$ are governed by the well-known Wigner-Eckart relations. In the case of infinitely-extended systems, with $G$ spontaneously broken, we prove that the corrections to such relations are provided by symmetry breaking Ward identities, and simply reduce to a tadpole term involving Goldstone bosons. The analysis extends to the case in which an explicit symmetry breaking term is present in the Hamiltonian, with the tadpole term now involving pseudo Goldstone bosons. An explicit example is discussed, illustrating the two cases.

quant-ph↗
arXiv2017

Symmetries of the dynamics and Noether theorem in classical mechanics

The aim of this note is to discuss the relation between one-parameter continuous symmetries of the dynamics, defined on physical grounds, and conservation laws. In the Hamiltonian formulation, such symmetries of the dynamics in general leave the Hamiltonian invariant only up to a total derivative $ d G(q)/d t$ . In this more general case, the corresponding formulation of Noether theorem gives that the conservation law displays a sort of ano\-ma\-ly, the constant of motion being the sum of the canonical generator of the symmetry transformations plus the generator $G$ of the gauge transformation $q_i \rightarrow q_i$, $p_i \rightarrow p_i - \partial G/ \partial q_i$.

physics.class-ph↗
arXiv2016

Existence of quantum time crystals

The existence of quantum time crystals is investigated and shown to be possible in pure phases defined by a state invariant under a group of space translations, as displayed by explicit examples.

quant-ph↗
arXiv2015

Gauge Invariance and Symmetry Breaking by Topology and Energy Gap

For the description of observables and states of a quantum system, it may be convenient to use a canonical Weyl algebra of which only a subalgebra $\mathcal A$, with a non-trivial center $\mathcal Z$, describes observables, the other Weyl operators playing the role of intertwiners between inequivalent representations of $\mathcal A$. In particular, this gives rise to a gauge symmetry described by the action of $\mathcal Z$. A distinguished case is when the center of the observables arises from the fundamental group of the manifold of the positions of the quantum system. Symmetries which do not commute with the topological invariants represented by elements of $\mathcal Z$ are then spontaneously broken in each irreducible representation of the observable algebra, compatibly with an energy gap; such a breaking exhibits a mechanism radically different from Goldstone and Higgs mechanisms. This is clearly displayed by the quantum particle on a circle, the Bloch electron and the two body problem.

math-ph↗
arXiv2015

Symmetries, Symmetry Breaking, Gauge Symmetries

The concepts of symmetry, symmetry breaking and gauge symmetries are discussed, their operational meaning being displayed by the observables {\em and} the (physical) states. For infinitely extended systems the states fall into physically disjoint {\em phases} characterized by their behavior at infinity or boundary conditions, encoded in the ground state, which provide the cause of symmetry breaking without contradicting Curie Principle. Global gauge symmetries, not seen by the observables, are nevertheless displayed by detectable properties of the states (superselected quantum numbers and parastatistics). Local gauge symmetries are not seen also by the physical states; they appear only in non-positive representations of field algebras. Their role at the Lagrangian level is merely to ensure the validity on the physical states of local Gauss laws, obeyed by the currents which generate the corresponding global gauge symmetries; they are responsible for most distinctive physical properties of gauge quantum field theories. The topological invariants of a local gauge group define superselected quantum numbers, which account for the $θ$ vacua.

physics.hist-ph↗
arXiv2006

Asymptotic Abelianness and Braided Tensor C*-Categories

By introducing the concepts of asymptopia and bi-asymptopia, we show how braided tensor C*-categories arise in a natural way. This generalizes constructions in algebraic quantum field theory by replacing local commutativity by suitable forms of asymptotic Abelianness.

math-ph↗
arXiv2000

Quantum delocalization of the electric charge

The classical Maxwell-Dirac and Maxwell-Klein-Gordon theories admit solutions of the field equations where the corresponding electric current vanishes in the causal complement of some bounded region of Minkowski space. This poses the interesting question of whether states with a similarly well localized charge density also exist in quantum electrodynamics. For a large family of charged states, the dominant quantum corrections at spacelike infinity to the expectation values of local observables are computed. It turns out that certain moments of the charge density decrease no faster than the Coulomb field in spacelike directions. In contrast to the classical theory, it is therefore impossible to define the electric charge support of these states in a meaningful way.

hep-th↗