Unambiguous one-loop quantum energies of 1+1 dimensional bosonic field configurations

Abstract

We calculate one-loop quantum energies in a renormalizable self-interacting theory in one spatial dimension by summing the zero-point energies of small oscillations around a classical field configuration, which need not be a solution of the classical field equations. We unambiguously implement standard perturbative renormalization using phase shifts and the Born approximation. We illustrate our method by calculating the quantum energy of a soliton/antisoliton pair as a function of their separation. This energy includes an imaginary part that gives a quantum decay rate and is associated with a level crossing in the solutions to the classical field equation in the presence of the source that maintains the soliton/antisoliton pair.

Email correspondence to [email protected] ; 10 pages, 2 figures, REVTeX, BoxedEPS; v2: Fixed description of level crossing as a function of $x_0$; v3: Fixed numerical error in figure data

Cited by in corpus (35)

• Casimir Effects in Renormalizable Quantum Field Theories
• Heavy Fermion Stabilization of Solitons in 1+1 Dimensions
• Quantum fluctuations of Wilson loops from string models
• One-loop surface tensions of (supersymmetric) kink domain walls from dimensional regularization
• Fermionic One-Loop Corrections to Soliton Energies in 1+1 Dimensions
• Two-Loop Scalar Kinks
• Derivative Expansion and Soliton Masses
• Vacuum Polarization Energy for General Backgrounds in One Space Dimension
• One-Loop Quantum Energy Densities of Domain Wall Field Configurations
• Once more on the BPS bound for the susy kink
• An Effective Field Theory for Fractional Quantum Hall Systems near $\nu =5/2$
• Excited Kinks as Quantum States
• The Two-Loop ${\varphi }^4$ Kink Mass
• Fermion-induced effective action in the presence of a static inhomogeneous magnetic field
• Effective Potential for Uniform Magnetic Fields through Pauli Interaction
• Quantum Effects of Solitons in the Self-Dual Impurity Model
• The self-consistent bounce: an improved nucleation rate
• Quantum Corrections to Solitons in the ${\Phi }^8$ Model
• Collective Coordinate Methods and Their Applicability to ${\phi }^4$ Models
• One loop renormalization of soliton quantum mass corrections in (1+1)-dimensional scalar field theory models
• Effective Energy Approach to Collectively Quantized Systems
• Variational Approach to Excited Fermions on Kinks
• Exact One-Loop Thermal Free Energies of Solitons
• Soliton vacuum energies and the CP(1) model
• Wilson loops from supergravity and string theory
• One-loop quantum correction to the mass of the supersymmetric Kink in (1 + 1) dimensions using the exact spectra and the phase shifts
• Comment on `One Loop Renormalization of Soliton Quantum Mass Corrections in 1+1 Dimensional Scalar Field Theory Models' (Phys. Lett. B542 (2002) 282 [hep-th/0206047])
• A note on one-loop soliton quantum mass corrections
• A supersymmetric exotic field theory in (1+1) dimensions. One loop soliton quantum mass corrections
• The Radiative Corrections to the Mass of the Kink Using an Alternative Renormalization Program
• Fermion Production in Strong Magnetic Field and its Astrophysical Implications
• The ${\varphi }^4$ Kink Mass at Two Loops
• One-loop quantum cosmological correction to the gravitational constant using the kink solution in de Sitter universe
• One-loop quantum cosmological correction to the gravitational constant in the closed Friedmann-Robertson-Walker universe
• One-loop Effective Actions in Shape-invariant Scalar Backgrounds