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Register a new userHigher Derivative Scalar Quantum Field Theory in Curved Spacetime
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We study a free scalar field $phi$ in a fixed curved background spacetime subject to a higher derivative field equation of the form $F(Box)phi =0$, where $F$ is a polynomial of the form $F(Box)= prod_i (Box-m_i^2)$ and all masses $m_i$ are distinct and real. Using an auxiliary field method to simplify the calculations, we obtain expressions for the Belinfante-Rosenfeld symmetric energy-momentum tensor and compare it with the canonical energy-momentum tensor when the background is Minkowski spacetime. We also obtain the conserved symplectic current necessary for quantisation and briefly discuss the issue of negative energy versus negative norm and its relation to Reflection Positivity in Euclidean treatments. We study, without assuming spherical symmetry, the possible existence of finite energy static solutions of the scalar equations, in static or stationary background geometries. Subject to various assumptions on the potential, we establish non-existence results including a no-scalar-hair theorem for static black holes. We consider Pais-Uhlenbeck field theories in a cosmological de Sitter background, and show how the Hubble friction may eliminate what would otherwise be unstable behaviour when interactions are included.
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Many-body systems with chiral fermions exhibit anomalous transport phenomena originated from quantum anomalies. Based on quantum field theory, we derive the kinetic theory for chiral fermions interacting with an external electromagnetic field and a background curved geometry. The resultant framework respects the covariance under the U(1) gauge, local Lorentz, and diffeomorphic transformations. It is particularly useful to study the gravitational or non-inertial effects for chiral systems. As the first application, we study the chiral dynamics in a rotating coordinate and clarify the roles of the Coriolis force and spin-vorticity coupling in generating the chiral vortical effect (CVE). We also show that the CVE is an intrinsic phenomenon of a rotating chiral fluid, and thus independent of observers frame.
We study space-time symmetries in scalar quantum field theory (including interacting theories) on static space-times. We first consider Euclidean quantum field theory on a static Riemannian manifold, and show that the isometry group is generated by o
ne-parameter subgroups which have either self-adjoint or unitary quantizations. We analytically continue the self-adjoint semigroups to one-parameter unitary groups, and thus construct a unitary representation of the isometry group of the associated Lorentzian manifold. The method is illustrated for the example of hyperbolic space, whose Lorentzian continuation is Anti-de Sitter space.
The final ringdown phase in a coalescence process is a valuable laboratory to test General Relativity and potentially constrain additional degrees of freedom in the gravitational sector. We introduce here an effective description for perturbations around spherically symmetric spacetimes in the context of scalar-tensor theories, which we apply to study quasi-normal modes for black holes with scalar hair. We derive the equations of motion governing the dynamics of both the polar and the axial modes in terms of the coefficients of the effective theory. Assuming the deviation of the background from Schwarzschild is small, we use the WKB method to introduce the notion of light ring expansion. This approximation is analogous to the slow-roll expansion used for inflation, and it allows us to express the quasinormal mode spectrum in terms of a small number of parameters. This work is a first step in describing, in a model independent way, how the scalar hair can affect the ringdown stage and leave signatures on the emitted gravitational wave signal. Potential signatures include the shifting of the quasi-normal spectrum, the breaking of isospectrality between polar and axial modes, and the existence of scalar radiation.
While no-hair theorems forbid isolated black holes from possessing permanent moments beyond their mass, electric charge, and angular momentum, research over the past two decades has demonstrated that a black hole interacting with a time-dependent background scalar field will gain an induced scalar charge. In this paper, we study this phenomenon from an effective field theory (EFT) perspective. We employ a novel approach to constructing the effective point-particle action for the black hole by integrating out a set of composite operators localized on its worldline. This procedure, carried out using the in-in formalism, enables a systematic accounting of both conservative and dissipative effects associated with the black holes horizon at the level of the action. We show that the induced scalar charge is inextricably linked to accretion of the background environment, as both effects stem from the same parent term in the effective action. The charge, in turn, implies that a black hole can radiate scalar waves and will also experience a fifth force. Our EFT correctly reproduces known results in the literature for massless scalars, but now also generalizes to massive real scalar fields, allowing us to consider a wider range of scenarios of astrophysical interest. As an example, we use our EFT to study the early inspiral of a black hole binary embedded in a fuzzy dark matter halo.
It is well known that loss of information about a system, for some observer, leads to an increase in entropy as perceived by this observer. We use this to propose an alternative approach to decoherence in quantum field theory in which the machinery of renormalisation can systematically be implemented: neglecting observationally inaccessible correlators will give rise to an increase in entropy of the system. As an example we calculate the entropy of a general Gaussian state and, assuming the observers ability to probe this information experimentally, we also calculate the correction to the Gaussian entropy for two specific non-Gaussian states.
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