[Paper Review] Soldering Formalism: Theory and Applications

C. Wotzasek|ArXiv.org|Jun 2, 1998

Black Holes and Theoretical Physics6 references17 citations

TL;DR

This paper introduces the soldering formalism as a systematic method to unify dual field theories—such as self- and anti-self-dual actions—into a single duality-invariant master action, incorporating quantum interference effects. By applying soldering to electromagnetic duality in 2D and 4D and to bosonization in 2D and 3D, it derives new physical results, including the emergence of massive modes in QED and the equivalence of chiral models to the Schwinger or Thirring models via quantum interference.

ABSTRACT

The soldering mechanism is a new technique to work with distinct manifestations of dualities that incorporates interference effects, leading to new physical results that includes quantum contributions. This approach was used to investigate the cases of electromagnetic dualities, and $D\geq 2$ bosonization. In the former context this technique is applied for the quantum mechanical harmonic oscillator, the scalar field theory in two dimensions and the Maxwell theory in four dimensions. The soldered actions in any dimension leads to a master action which is duality invariant under a much bigger set of symmetries. The effects of coupling to gravity are also elaborated. In the later context, a technique is developed that solders the dual aspects of some symmetry following from the bosonisation of two distinct fermionic models, leading to new results which cannot be otherwise obtained. Exploiting this technique, the two dimensional chiral determinants with opposite chirality are soldered to reproduce either the usual gauge invariant expression leading to the Schwinger model or, alternatively, the Thirring model. Likewise, two apparently independent three dimensional massive Thirring models with same coupling but opposite mass signatures, in the long wavelegth limit, combine by the process of bosonisation and soldering to yield an effective massive Maxwell theory. The current bosonisation formulas are given, both in the original independent formulation as well as the effective theory, and shown to yield consistent results for the correlation functions.

Motivation & Objective

• To develop a systematic method for constructing duality-symmetric actions in any spacetime dimension.
• To unify distinct manifestations of duality symmetry—such as self- and anti-self-dual actions—into a single master action that includes quantum interference effects.
• To apply the soldering formalism to electromagnetic duality in 2D and 4D, and to bosonization in 2D and 3D, to derive new physical results.
• To clarify the role of Bose symmetry and gauge invariance in resolving bosonization ambiguities in chiral models.
• To show that two independent quantum field theories with dual symmetries can be combined into a single effective theory through bosonization and soldering.

Proposed method

• The soldering formalism combines two duality-related actions (e.g., self- and anti-self-dual) into a master action that is invariant under a larger duality group.
• The method uses a generalized internal two-dimensional space to define duality in even dimensions D=2k+2, enabling a unified treatment of duality symmetry.
• For bosonization, the formalism applies the soldering mechanism to dual chiral fermionic models, fusing them into a single effective theory.
• The approach incorporates quantum interference by treating the two dual actions as interfering components in the master action.
• Gauge and Bose symmetry are imposed as constraints to uniquely select physical solutions from the one-parameter family of bosonization ambiguities.
• The formalism is applied to the harmonic oscillator, 2D scalar field, Maxwell theory, and 3D massive Thirring models, with results verified via correlation functions.

Experimental results

Research questions

• RQ1 How can duality-symmetric actions be systematically constructed in arbitrary spacetime dimensions?
• RQ2 What physical effects arise from quantum interference between self- and anti-self-dual field theories?
• RQ3 How does the soldering formalism resolve the ambiguity in bosonization of chiral fermionic models?
• RQ4 Can two independent quantum field theories with dual symmetries be unified into a single effective theory?
• RQ5 What is the role of Bose symmetry in selecting gauge-invariant outcomes from bosonization?

Key findings

• The soldering formalism produces a master action that is invariant under a larger duality group than standard duality symmetries, incorporating quantum interference effects.
• In the 2D harmonic oscillator, the formalism reveals duality as a fundamental feature underlying all field theories, with quantum interference manifesting like in a double-slit experiment.
• For 2D chiral models, soldering of left- and right-moving modes reproduces both the gauge-invariant Schwinger model and the Thirring model, depending on parametrization.
• Imposing Bose symmetry uniquely selects the Jackiw-Rajaraman parameter a=1, resolving the bosonization ambiguity and ensuring gauge invariance.
• In 3D, two massive Thirring models with opposite mass signatures, when bosonized and soldered, yield an effective massive Maxwell theory in the long-wavelength limit.
• Correlation functions computed in the original models and in the effective theory (massive Maxwell) are identical, confirming consistency across the soldering procedure.