Symplectic realization of two interacting spin-two fields in three dimensions
arXiv:2005.00073 · doi:10.1007/JHEP01(2021)089
Abstract
We constructed a symplectic realization of the dynamic structure of two interacting spin-two fields in three dimensions. A significant simplification refers to the treatment of constraints: instead of performing a Hamiltonian analysis Dirac, we worked out a method that only uses properties of the pre-symplectic two-form matrix and its corresponding zero-modes to investigate the nature of constraints and the gauge structure of the theory. For instance, we demonstrate that the contraction of the zero-modes with the potential gradient, yields explicit expressions for the whole set of constraints on the dynamics of the theory, including the symmetrization condition and an explicit relationship between the coupling and cosmological constants. This way, we further identify the necessary conditions for the existence of a unique non-linear candidate for a partially massless theory, using only the expression for the interaction parameters of the model. In the case of gauge structure, the transformation laws for the entire set of dynamical variables are more straightforwardly derived from the structure of the remaining zero-modes; in this sense, the zero-modes must be viewed as the generators of the corresponding gauge transformations. Thereafter, we use an appropriate gauge-fixing procedure, the time gauge, to compute both the quantization brackets and the functional measure on the path integral associated with our model. Finally, we confirm that three-dimensional bi-gravity has two physical degrees of freedom per space point. With the above, we provide a new perspective for a better understanding of the dynamical structure of theories of interacting spin-two fields, which does not require the constraints to be catalogued as first- and second-class ones as in the case of Dirac's standard method.
References in corpus (42)
- Particle Dark Matter: Evidence, Candidates and Constraints
- Modified Gravity and Cosmology
- Dark Energy and the Accelerating Universe
- Resummation of Massive Gravity
- Generalization of the Fierz-Pauli Action
- Bimetric Gravity from Ghost-free Massive Gravity
- Resolving the Ghost Problem in non-Linear Massive Gravity
- Quantum Gravity Partition Functions in Three Dimensions
- Photon and Graviton Mass Limits
- Confirmation of the Secondary Constraint and Absence of Ghost in Massive Gravity and Bimetric Gravity
- Ghost-free Massive Gravity with a General Reference Metric
- Geometrical Description of the Fractional Quantum Hall Effect
- Partial Masslessness of Higher Spins in (A)dS
- Interacting Spin-2 Fields
- Gauge Invariances and Phases of Massive Higher Spins in (A)dS
- Dark Energy and Dark Gravity
- Ghost free Massive Gravity in the Stückelberg language
- Stability of Massive Cosmological Gravitons
- Beyond Amplitudes' Positivity and the Fate of Massive Gravity
- Heavy spin-2 Dark Matter
- A note on "symmetric" vielbeins in bimetric, massive, perturbative and non perturbative gravities
- Gravitational Origin of Dark Matter
- Bimetric Theory of Fractional Quantum Hall States
- The Constraint Algebra of Topologically Massive AdS Gravity
- Zwei-Dreibein Gravity
- Renormalizability of Massive Gravity in Three Dimensions
- Note About Hamiltonian Structure of Non-Linear Massive Gravity
- On the local structure of spacetime in ghost-free bimetric theory and massive gravity
- Bimetric Theory and Partial Masslessness with Lanczos-Lovelock Terms in Arbitrary Dimensions
- The Boulware-Deser mode in Zwei-Dreibein gravity
- Canonical structure of Tetrad Bimetric Gravity
- Self-interacting Spin-2 Dark Matter
- Analysis of constraints and their algebra in bimetric theory
- Faddeev-Jackiw quantization and the path integral
- Partially Massless Graviton on Beyond Einstein Spacetimes
- Ashtekar's Variables for Arbitrary Gauge Group
- Interacting spin-2 fields in three dimensions
- Lagrangian approach to a symplectic formalism for singular systems
- Is Bimetric Gravity Really Ghost Free?
- Hamiltonian Formalism of General Bimetric Gravity
- On the Faddeev-Jackiw Symplectic Framework for Topologically Massive Gravity
- Gauge symmetry and constraints structure in topologically massive AdS gravity: A symplectic viewpoint