Supersymmetric Field-Theoretic Models on a Supermanifold

We propose the extension of some structural aspects that have successfully been applied in the development of the theory of quantum fields propagating on a general spacetime manifold so as to include superfield models on a supermanifold. We only deal with the limited class of supermanifolds which admit the existence of a smooth body manifold structure. Our considerations are based on the Catenacci-Reina-Teofillatto-Bryant approach to supermanifolds. In particular, we show that the class of supermanifolds constructed by Bonora-Pasti-Tonin satisfies the criterions which guarantee that a supermanifold admits a Hausdorff body manifold. This construction is the closest to the physicist's intuitive view of superspace as a manifold with some anticommuting coordinates, where the odd sector is topologically trivial. The paper also contains a new construction of superdistributions and useful results on the wavefront set of such objects. Moreover, a generalization of the spectral condition is formulated using the notion of the wavefront set of superdistributions, which is equivalent to the requirement that all of the component fields satisfy, on the body manifold, a microlocal spectral condition proposed by Brunetti-Fredenhagen-K\"ohler.Comment: Final version to appear in J.Math.Phy

Equivalence of the (generalised) Hadamard and microlocal spectrum condition for (generalised) free fields in curved spacetime

We prove that the singularity structure of all n-point distributions of a state of a generalised real free scalar field in curved spacetime can be estimated if the two-point distribution is of Hadamard form. In particular this applies to the real free scalar field and the result has applications in perturbative quantum field theory, showing that the class of all Hadamard states is the state space of interest. In our proof we assume that the field is a generalised free field, i.e. that it satisies scalar (c-number) commutation relations, but it need not satisfy an equation of motion. The same argument also works for anti-commutation relations and it can be generalised to vector-valued fields. To indicate the strengths and limitations of our assumption we also prove the analogues of a theorem by Borchers and Zimmermann on the self-adjointness of field operators and of a very weak form of the Jost-Schroer theorem. The original proofs of these results in the Wightman framework make use of analytic continuation arguments. In our case no analyticity is assumed, but to some extent the scalar commutation relations can take its place.Comment: 18 page

Axiomatic quantum field theory in curved spacetime

The usual formulations of quantum field theory in Minkowski spacetime make crucial use of features--such as Poincare invariance and the existence of a preferred vacuum state--that are very special to Minkowski spacetime. In order to generalize the formulation of quantum field theory to arbitrary globally hyperbolic curved spacetimes, it is essential that the theory be formulated in an entirely local and covariant manner, without assuming the presence of a preferred state. We propose a new framework for quantum field theory, in which the existence of an Operator Product Expansion (OPE) is elevated to a fundamental status, and, in essence, all of the properties of the quantum field theory are determined by its OPE. We provide general axioms for the OPE coefficients of a quantum field theory. These include a local and covariance assumption (implying that the quantum field theory is locally and covariantly constructed from the spacetime metric), a microlocal spectrum condition, an "associativity" condition, and the requirement that the coefficient of the identity in the OPE of the product of a field with its adjoint have positive scaling degree. We prove curved spacetime versions of the spin-statistics theorem and the PCT theorem. Some potentially significant further implications of our new viewpoint on quantum field theory are discussed.Comment: Latex, 44 pages, 2 figure

Batalin-Vilkovisky formalism in perturbative algebraic quantum field theory

On the basis of a thorough discussion of the Batalin-Vilkovisky formalism for classical field theory presented in our previous publication, we construct in this paper the Batalin-Vilkovisky complex in perturbatively renormalized quantum field theory. The crucial technical ingredient is a proof that the renormalized time-ordered product is equivalent to the pointwise product of classical field theory. The renormalized Batalin-Vilkovisky algebra is then the classical algebra but written in terms of the time-ordered product, together with an operator which replaces the ill defined graded Laplacian of the unrenormalized theory. We identify it with the anomaly term of the anomalous Master Ward Identity of Brennecke and D\"utsch. Contrary to other approaches we do not refer to the path integral formalism and do not need to use regularizations in intermediate steps.Comment: 34 page

Conformal generally covariant quantum field theory: The scalar field and its Wick products

In this paper we generalize the construction of generally covariant quantum theories given in the work of Brunetti, Fredenhagen and Verch to encompass the conformal covariant case. After introducing the abstract framework, we discuss the massless conformally coupled Klein Gordon field theory, showing that its quantization corresponds to a functor between two certain categories. At the abstract level, the ordinary fields, could be thought as natural transformations in the sense of category theory. We show that, the Wick monomials without derivatives (Wick powers), can be interpreted as fields in this generalized sense, provided a non trivial choice of the renormalization constants is given. A careful analysis shows that the transformation law of Wick powers is characterized by a weight, and it turns out that the sum of fields with different weights breaks the conformal covariance. At this point there is a difference between the previously given picture due to the presence of a bigger group of covariance. It is furthermore shown that the construction does not depend upon the scale mu appearing in the Hadamard parametrix, used to regularize the fields. Finally, we briefly discuss some further examples of more involved fields.Comment: 21 pages, comments added, to appear on Commun. Math. Phy

Hadamard states from null infinity

Free field theories on a four dimensional, globally hyperbolic spacetime, whose dynamics is ruled by a Green hyperbolic partial differential operator, can be quantized following the algebraic approach. It consists of a two-step procedure: In the first part one identifies the observables of the underlying physical system collecting them in a *-algebra which encodes their relational and structural properties. In the second step one must identify a quantum state, that is a positive, normalized linear functional on the *-algebra out of which one recovers the interpretation proper of quantum mechanical theories via the so-called Gelfand-Naimark-Segal theorem. In between the plethora of possible states, only few of them are considered physically acceptable and they are all characterized by the so-called Hadamard condition, a constraint on the singular structure of the associated two-point function. Goal of this paper is to outline a construction scheme for these states which can be applied whenever the underlying background possesses a null (conformal) boundary. We discuss in particular the examples of a real, massless conformally coupled scalar field and of linearized gravity on a globally hyperbolic and asymptotically flat spacetime.Comment: 23 pages, submitted to the Proceedings of the conference "Quantum Mathematical Physics", held in Regensburg from the 29th of September to the 02nd of October 201

Dynamical locality of the free scalar field

Dynamical locality is a condition on a locally covariant physical theory, asserting that kinematic and dynamical notions of local physics agree. This condition was introduced in [arXiv:1106.4785], where it was shown to be closely related to the question of what it means for a theory to describe the same physics on different spacetimes. In this paper, we consider in detail the example of the free minimally coupled Klein--Gordon field, both as a classical and quantum theory (using both the Weyl algebra and a smeared field approach). It is shown that the massive theory obeys dynamical locality, both classically and in quantum field theory, in all spacetime dimensions $n\ge 2$ and allowing for spacetimes with finitely many connected components. In contrast, the massless theory is shown to violate dynamical locality in any spacetime dimension, in both classical and quantum theory, owing to a rigid gauge symmetry. Taking this into account (equivalently, working with the massless current) dynamical locality is restored in all dimensions $n\ge 2$ on connected spacetimes, and in all dimensions $n\ge 3$ if disconnected spacetimes are permitted. The results on the quantized theories are obtained using general results giving conditions under which dynamically local classical symplectic theories have dynamically local quantizations.Comment: 34pp, LaTeX2e. Version to appear in Annales Henri Poincar

The Mathematical Universe

I explore physics implications of the External Reality Hypothesis (ERH) that there exists an external physical reality completely independent of us humans. I argue that with a sufficiently broad definition of mathematics, it implies the Mathematical Universe Hypothesis (MUH) that our physical world is an abstract mathematical structure. I discuss various implications of the ERH and MUH, ranging from standard physics topics like symmetries, irreducible representations, units, free parameters, randomness and initial conditions to broader issues like consciousness, parallel universes and Godel incompleteness. I hypothesize that only computable and decidable (in Godel's sense) structures exist, which alleviates the cosmological measure problem and help explain why our physical laws appear so simple. I also comment on the intimate relation between mathematical structures, computations, simulations and physical systems.Comment: Replaced to match accepted Found. Phys. version, 31 pages, 5 figs; more details at http://space.mit.edu/home/tegmark/toe.htm

Gaia white dwarfs within 40 pc I : spectroscopic observations of new candidates

We present a spectroscopic survey of 230 white dwarf candidates within 40 pc of the Sun from the William Herschel Telescope and Gran Telescopio Canarias. All candidates were selected from Gaia Data Release 2 (DR2) and in almost all cases had no prior spectroscopic classifications. We find a total of 191 confirmed white dwarfs and 39 main-sequence star contaminants. The majority of stellar remnants in the sample are relatively cool (〈Teff〉 = 6200 K), showing either hydrogen Balmer lines or a featureless spectrum, corresponding to 89 DA and 76 DC white dwarfs, respectively. We also recover two DBA white dwarfs and 9–10 magnetic remnants. We find two carbon-bearing DQ stars and 14 new metal-rich white dwarfs. This includes the possible detection of the first ultra-cool white dwarf with metal lines. We describe three DZ stars for which we find at least four different metal species, including one which is strongly Fe- and Ni-rich, indicative of the accretion of a planetesimal with core-Earth composition. We find one extremely massive (1.31 ± 0.01 M⊙) DA white dwarf showing weak Balmer lines, possibly indicating stellar magnetism. Another white dwarf shows strong Balmer line emission but no infrared excess, suggesting a low-mass sub-stellar companion. High spectroscopic completeness (>99%) has now been reached for Gaia DR2 sources within 40 pc sample, in the northern hemisphere (δ > 0 deg) and located on the white dwarf cooling track in the Hertzsprung-Russell diagram. A statistical study of the full northern sample is presented in a companion paper

Two decades of optical timing of the shortest-period binary star system HM Cancri

The shortest-period binary star system known to date, RX J0806.3+1527 (HM Cancri), has now been observed in the optical for more than two decades. Although it is thought to be a double degenerate binary undergoing mass transfer, an early surprise was that its orbital frequency, f0, is currently increasing as the result of gravitational wave radiation. This is unusual since it was expected that the mass donor was degenerate and would expand on mass loss, leading to a decreasing f0. We exploit two decades of high-speed photometry to precisely quantify the trajectory of HM Cancri, allowing us to find that f¨0 is negative, where f¨0 = (−5.38±2.10)×10−27 Hz s−2. Coupled with our positive frequency derivative, we show that mass transfer is counteracting gravitational-wave dominated orbital decay and that HM Cancri will turn around within 2100 ± 800 yr from now. We present Hubble Space Telescope ultra-violet spectra which display Lyman-α absorption, indicative of the presence of hydrogen accreted from the donor star. We use these pieces of information to explore a grid of permitted donor and accretor masses with the Modules for Experiments in Stellar Astrophysics suite, finding models in good accordance with many of the observed properties for a cool and initially hydrogen-rich extremely low mass white dwarf (≈0.17 M⊙) coupled with a high-accretor mass white dwarf (≈1.0 M⊙). Our measurements and models affirm that HM Cancri is still one of the brightest verification binaries for the Laser Interferometer Space Antenna spacecraft