[Paper Review] Torsion: theory and possible observables

Ilya L. Shapiro|ArXiv.org|Nov 9, 1998

Relativity and Gravitational Theory3 references3 citations

TL;DR

This paper investigates the quantum field theory of gravity with torsion, showing that torsion couples to spinor and scalar (Higgs) fields via nonminimal interactions to ensure renormalizability. It identifies new torsion-dependent terms in the Pauli and nonrelativistic equations for spin-1/2 particles, and demonstrates that effective field theory for torsion in the Standard Model is inconsistent due to Higgs-induced symmetry breaking, with phenomenological implications for Planck-scale torsion masses.

ABSTRACT

We discuss the theoretical basis for the search of the possible experimental manifestations of the torsion field at low energies. First, the quantum field theory in an external gravitational field with torsion is reviewed. The renormalizability requires the nonminimal interaction of torsion with spinor and scalar (Higgs) fields. The Pauli-like equation contains new torsion-dependent terms which have a different structure as compared with the standard electromagnetic ones. The same concerns the nonrelativistic equations for spin-${1}/{2}$ particle in an external torsion and electromagnetic fields. Second, we discuss the propagating torsion. For the Dirac spinor coupled to the electromagnetic and torsion field there is some additional softly broken local symmetry associated with torsion. As a consequence of this symmetry, in the framework of effective field theory, the torsion action is fixed with accuracy to the values of the coupling constant of the torsion-spinor interaction, mass of the torsion and higher derivative terms. The introduction of the Higgs field spoils the consistency of this scheme, and the effective quantum field theory for torsion embedded into the Standard Model is not possible. The phenomenological consequences of the torsion-fermion interaction are drown and the case of the torsion mass of the Planck order is discussed.

Motivation & Objective

• To establish the theoretical framework for low-energy experimental detection of torsion in gravity.
• To analyze the renormalizability of quantum field theory in a gravitational background with torsion.
• To investigate the structure of equations of motion for spin-1/2 particles in the presence of torsion and electromagnetic fields.
• To assess the viability of an effective field theory for torsion within the Standard Model framework.
• To explore phenomenological consequences of torsion-fermion interactions, particularly for Planck-scale torsion masses.

Proposed method

• Reviews quantum field theory in a gravitational background with torsion, emphasizing the role of nonminimal coupling for renormalizability.
• Derives modified Pauli and nonrelativistic equations for spin-1/2 particles, identifying new torsion-dependent terms distinct from electromagnetic interactions.
• Identifies a softly broken local symmetry associated with torsion in the Dirac field coupled to torsion and electromagnetic fields.
• Uses effective field theory to constrain the torsion action, fixing it up to coupling constants, torsion mass, and higher-derivative terms.
• Analyzes the inconsistency of embedding torsion into the Standard Model by introducing the Higgs field, which breaks the symmetry and invalidates the effective theory.
• Applies phenomenological analysis to predict observable effects of torsion, particularly for torsion masses on the order of the Planck scale.

Experimental results

Research questions

• RQ1 How does torsion modify the dynamics of spin-1/2 particles in external electromagnetic and gravitational fields?
• RQ2 What are the conditions under which quantum field theory with torsion remains renormalizable?
• RQ3 Can an effective field theory description of torsion be consistently embedded into the Standard Model?
• RQ4 What are the phenomenological signatures of a Planck-scale torsion field in low-energy experiments?
• RQ5 How does the introduction of the Higgs field affect the symmetry structure and consistency of torsion-based field theories?

Key findings

• The inclusion of nonminimal coupling between torsion and spinor/scalar fields is required for renormalizability in quantum field theory with torsion.
• The Pauli equation acquires new torsion-dependent terms with a structure fundamentally different from electromagnetic interactions.
• A softly broken local symmetry emerges in the Dirac field coupled to torsion and electromagnetic fields, constraining the form of the torsion action in effective field theory.
• The presence of the Higgs field breaks the symmetry underlying the effective torsion action, rendering a consistent effective quantum field theory for torsion within the Standard Model impossible.
• Phenomenological analysis suggests that torsion with a mass on the order of the Planck scale could yield observable effects in low-energy experiments.
• The modified equations of motion for spin-1/2 particles in torsion fields predict measurable deviations from standard quantum mechanical behavior, particularly in spin precession and energy level shifts.