Symmetries and propagator in multifractional scalar field theory
arXiv:1210.2754 · doi:10.1103/PhysRevD.87.085008
Abstract
The symmetries of a scalar field theory in multifractional spacetimes are analyzed. The free theory realizes the Poincaré algebra, and the associated symmetries are modifications of ordinary translations and Lorentz transformations. In the interacting case, the Poincaré algebra is broken by interaction terms. The Feynman propagator of the scalar field is computed and found to possess the usual mass poles. As a consequence of these findings, the mass of a particle is a well-defined concept at all scales, and a perturbative quantum theory can be constructed.
arXiv comment15 pages, 1 double figure. v2-3: discussion improved, results unchanged, typos corrected
References in corpus (46)
- Quantum Gravity at a Lifshitz Point
- Spectral Dimension of the Universe in Quantum Gravity at a Lifshitz Point
- Towards singularity and ghost free theories of gravity
- Super-renormalizable Quantum Gravity
- Discrete scale invariance and complex dimensions
- Spectral Dimension of the Universe
- Gravity and the standard model with neutrino mixing
- Fractional Vector Calculus and Fractional Maxwell's Equations
- Fractal universe and quantum gravity
- Fractal Spacetime Structure in Asymptotically Safe Gravity
- Lorentz symmetry breaking as a quantum field theory regulator
- Continuous Medium Model for Fractal Media
- Quantum field theory, gravity and cosmology in a fractal universe
- Fractal properties of quantum spacetime
- Fractal Structure of Loop Quantum Gravity
- Noncommutative Geometry and the standard model with neutrino mixing
- Renormalization of Lorentz violating theories
- Geometry and field theory in multi-fractional spacetime
- Spectral geometry as a probe of quantum spacetime
- Renormalization group in Lifshitz-type theories
- Spontaneous Dimensional Reduction in Short-Distance Quantum Gravity?
- Spectral dimension of a quantum universe
- Non-commutative Renormalization
- Fractal space-times under the microscope: A Renormalization Group view on Monte Carlo data
- Trace Anomaly in Quantum Spacetime Manifold
- Fractional Differential Forms
- Spectral dimension as a probe of the ultraviolet continuum regime of causal dynamical triangulations
- Thermodynamics of photons on fractals
- Gravity on a multifractal
- Wave Equation for Fractal Solid String
- Diffusion in multiscale spacetimes
- Possible Experimental Test of Continuous Medium Model for Fractal Media
- Weighted scale invariant quantum field theories
- Fractional and noncommutative spacetimes
- Physical Consequences of Complex Dimensions of Fractals
- Quantum mechanics in fractional and other anomalous spacetimes
- Anomalous dimension in semiclassical gravity
- Discrete to continuum transition in multifractal spacetimes
- Diffusion in quantum geometry
- Primordial Black Hole Evaporation and Spontaneous Dimensional Reduction
- The Hidden Quantum Groups Symmetry of Super-renormalizable Gravity
- Dynamical dimensional reduction in toy models of 4D causal quantum gravity
- Introduction to multifractional spacetimes
- Multigraph models for causal quantum gravity and scale dependent spectral dimension
- Unitary Standard Model from Spontaneous Dimensional Reduction and Weak Boson Scattering at the LHC
- Spontaneous Spacetime Reduction and Unitary Weak Boson Scattering at the LHC
Cited by in corpus (11)
- Multifractional theories: an unconventional review
- Multi-scale gravity and cosmology
- Multifractional theories: an updated review
- Spectral dimension and diffusion in multi-scale spacetimes
- Multifractional spacetimes, asymptotic safety and Hořava-Lifshitz gravity
- Varying electric charge in multiscale spacetimes
- Quantum field theory with varying couplings
- Deformed symmetries in noncommutative and multifractional spacetimes
- Standard Model in multiscale theories and observational constraints
- Relativistic particle in multiscale spacetimes
- On observational signatures of multi-fractional theory