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T. A. Larsson

Publications and source records attributed to T. A. Larsson.

At least 19 recordsLinked to original sources
arXiv2015

Three Principles for Quantum Gravity

We postulate that the fundamental principles of Quantum Gravity are diffeomorphism symmetry, unitarity, and locality. Local observables are compatible with diffeomorphism symmetry in the presence of diff anomalies, which modify the symmetry algebra upon quantization. We describe the generalization of the Virasoro extension to the diffeomorphism algebra in several dimensions, and its off-shell representations. These anomalies can not arise in QFT, because the Virasoro-like cocycles are functionals of the observer's spacetime trajectory, which is not present in QFT. Possible implications for physics are discussed.

gr-qc↗
arXiv2015

New Derivation of Off-Shell Representations of the Multi-dimensional Affine and Virasoro Algebras

Algebras of currents and diffeomorphisms in arbitrary dimension have extensions which generalize the affine and Virasoro algebras on the circle. A large class of off-shell representations was discovered in Comm. Math. Phys. 214 (2000) 469--491. That paper is not so accessible due to a slightly non-standard normal ordering formalism and cumbersome $p$-jet calculations. The purpose of the present paper is to simplify the derivation using standard OPE methods and a more field-like formalism.

math-ph↗
arXiv2014

Covariant Mickelsson-Faddeev extensions of gauge and diffeomorphism algebras

We construct new extensions of current and diffeomorphism algebras in N>3 dimensions, which are related to the Mickelsson-Faddeev algebra. The result is compatible with Dzhumadil'daev's classification of diffeomorphism cocycles. We also construct an extension of the current algebra in N>=5 dimensions which depends on the fourth Casimir operator.

physics.gen-ph↗
arXiv2009

QJT as a Regularization: Origin of the New Gauge Anomalies

QJT is considered as a regularization of QFT, where the fields are replaced by finite $p$-jets. The regularized phase space is infinite-dimensional, because not all histories are determined by initial conditions. Gauge symmetries are not fully preserved by the regularization, and gauge anomalies arise. These anomalies are of a new type, not present in QFT. They generically diverge when the regulator is removed, but can be made finite with a particular choice of field content, provided that spacetime has at most four dimensions. The field content appears to include unphysical fields that violate the spin-statistics theorem.

physics.gen-ph↗
arXiv2008

The physical observer I: Absolute and relative fields

Quantum Jet Theory (QJT) is a deformation of QFT where also the quantum dynamics of the observer is taken into account. This is achieved by introducing relative fields, labelled by locations measured by rods relative to the observer's position. In the Hamiltonian formalism, the observer's momentum is modified: p_i \to p_i - P_i, where P_i is the momentum carried by the field quanta. The free scalar field, free electromagnetism and gravity are treated as examples. Standard QFT results are recovered in the limit that the observer's mass M \to \infty and its charge e \to 0. This limit is well defined except for gravity, because e = M in that case (heavy mass equals inert mass). In a companion paper we describe how QJT also leads to new observer-dependent gauge and diff anomalies, which can not be formulated within QFT proper.

physics.gen-ph↗
arXiv2008

The physical observer II: Gauge and diff anomalies

In a companion paper we studied field theory in the presence of a physical observer with quantum dynamics. Here we describe the most striking consequence of this assumption: new gauge and diff anomalies arise. The relevant cocycles depend on the observer's spacetime trajectory and can hence not appear in QFT, where this quantity is never introduced. Diff anomalies necessarily arise in every locally nontrivial, non-holographic theory of quantum gravity. Cancellation of the divergent parts of the anomalies only works if spacetime has four dimensions.

physics.gen-ph↗
arXiv2007

A BV subtlety

The standard BV complex is never acyclic provided that the equations of motion have solutions and the admissible class of functions is general enough, unless one introduces second-order antifields. This phenomenon is explicitly illustrated for the harmonic oscillator and the free electromagnetic field.

math-ph↗
arXiv2007

Multi-dimensional Virasoro algebra and quantum gravity

I review the multi-dimensional generalizations of the Virasoro algebra, i.e. the non-central Lie algebra extensions of the algebra vect(N) of general vector fields in N dimensions, and its Fock representations. Being the Noether symmetry of background independent theories such as N-dimensional general relativity, this algebra is expected to be relevant to the quantization of gravity. To this end, more complicated modules which depend on dynamics in the form of Euler-Lagrange equations are described. These modules can apparently only be interpreted as quantum fields if spacetime has four dimensions and both bosons and fermions are present.

hep-th↗
arXiv2007

Manifestly covariant canonical quantization of gravity and diffeomorphism anomalies in four dimensions

Canonical quantization of gravity requires knowledge about the representation theory of its constraint algebra, which is physically equivalent to the algebra of arbitrary 4-diffeomorphisms. All interesting lowest-energy representations are projective, making the relevant algebra into a four-dimensional generalization of the Virasoro algebra. Such diffeomorphism anomalies are invisible in field theory, because the relevant cocycles are functionals of the observer's trajectory in spacetime. The multi-dimensional Virasoro algebra acts naturally in the phase space of arbitrary histories, with dynamics playing the role of first-class constraints. General relativity is regularized by expanding all fields in Taylor series around the observer's trajectory, and truncating at some fixed order. This regularized but manifestly general-covariant theory is quantized in the history phase space, and dynamics is imposed afterwards, in analogy with BRST quantization. Infinities arise when the regularization is removed; it is presently unclear how these should be dealt with.

hep-th↗
arXiv2007

Quantum Jet Theory I: Free fields

QJT (Quantum Jet Theory) is the quantum theory of jets, which can be canonically identified with truncated Taylor series. Ultralocality requires a novel quantization scheme, where dynamics is treated as a constraint in the history phase space. QJT differs from QFT since it involves a new datum: the expansion point. This difference is substantial because it leads to new gauge and diff anomalies, which are necessary to combine background independence with locality. Physically, the new ingredient is that the observer's trajectory is explicitly introduced and quantized together with the fields. In this paper the harmonic oscillator and free fields are treated within QJT, correcting previous flaws. The standard Hilbert space is recovered for the harmonic oscillator, but there are interesting modifications already for the free scalar field, due to quantization of the observer's trajectory. Only free fields are treated in detail, but the complications when interactions are introduced are briefly discussed. We also explain why QJT is necessary to resolve the conceptual problems of quantum gravity.

hep-th↗
arXiv2006

Local, global, divergent - which gauge symmetries are redundant?

A local gauge symmetry can not possibly be a mere redundancy of the description, provided that 1. charge is nonzero. 2. we also consider divergent gauge transformations, whose brackets with local transformations contain global charge operators. If these conditions hold, unitarity requires the existence of gauge anomalies. We describe the relevant multi-dimensional generalization of affine Kac-Moody algebras, explain why it only arises if the observer's trajectory is explicitly introduced, and contrast it to the Mickelsson-Faddeev algebra which pertains to chiral-fermion type anomalies.

math-ph↗
arXiv2005

On the problem of time in two and four dimensions

In general-covariant theories the Hamiltonian is a constraint, and hence there is no time evolution; this is the problem of time. In the subcritical free string, the Hamiltonian ceases to be a constraint after quantization due to conformal anomalies, and time evolution becomes non-trivial and unitary. It is argued that the problem of time in four dimensions can be resolved by a similar mechanism. This forces us to challenge some widespread beliefs, such as the idea that every gauge symmetry is a redundancy of the description.

hep-th↗
arXiv2005

Manifestly covariant canonical quantization III: Gravity, locality, and diffeomorphism anomalies in four dimensions

The recently introduced manifestly covariant canonical quantization scheme is applied to gravity. New diffeomorphism anomalies generating a multi-dimensional generalization of the Virasoro algebra arise. This does not contradict theorems about the non-existence of gravitational anomalies in four dimensions, because the relevant cocycles depend on the observer's spacetime trajectory, which is ignored in conventional field theory. Rather than being inconsistent, these anomalies are necessary to obtain a {\em local} theory of quantum gravity.

hep-th↗
arXiv2005

Manifestly covariant canonical quantization II: Gauge theory and anomalies

In hep-th/0411028 a new manifestly covariant canonical quantization method was developed. The idea is to quantize in the phase space of arbitrary histories first, and impose dynamics as first-class constraints afterwards. The Hamiltonian is defined covariantly as the generator of rigid translations of the fields relative to the observer. This formalism is now applied to theories with gauge symmetries, in particular electromagnetism and Yang-Mills theory. The gauge algebra acquires an abelian extension proportional to the quadratic Casimir operator. Unlike conventional gauge anomalies proportional to the third Casimir, this is not inconsistent. On the contrary, a well-defined and non-zero charge operator is only compatible with unitarity in the presence of such anomalies. This anomaly is invisible in field theory because it is a functional of the observer's trajectory, which is conventionally ignored.

hep-th↗
arXiv2004

Manifestly covariant canonical quantization I: the free scalar field

Classical physics is reformulated as a constrained Hamiltonian system in the history phase space. Dynamics, i.e. the Euler-Lagrange equations, play the role of first-class constraints. This allows us to apply standard methods from the theory of constrained Hamiltonian systems, e.g. Dirac brackets and cohomological methods. In analogy with BRST quantization, we quantize in the history phase space first and impose dynamics afterwards. To obtain a truly covariant formulation, all fields must be expanded in a Taylor series around the observer's trajectory, which acquires the status of a quantized physical field. The formalism is applied to the harmonic oscillator and to the free scalar field. Standard results are recovered, but only in the approximation that the observer's trajectory is treated as a classical curve.

hep-th↗
arXiv2004

A diffeomorphism anomaly in every dimension

Field-theoretic pure gravitational anomalies only exist in $4k+2$ dimensions. However, canonical quantization of non-field-theoretic systems may give rise to diffeomorphism anomalies in any number of dimensions. I present a simple example, where a higher-dimensional generalization of the Virasoro algebra arises upon quantization.

hep-th↗