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A bstract Effective field theories (EFT) are strongly constrained by fundamental principles such as unitarity, locality, causality, and Lorentz invariance. In this paper, we consider the EFT of photons (or other U(1) gauge field) and compare different approaches to obtain bounds on its Wilson coefficients. We present an analytic derivation of the implications of unitarity (linear and non-linear positivity bounds) and compare these constraints with the requirement of causal propagation of the photon modes around non-trivial backgrounds generated by external sources. Within this setup, we find that the low energy causality condition can give complementary constraints to our analytic positivity bounds. In other words, simple analytic techniques can give strong constraints on the allowed region of the photon EFT parameters even when the positivity bounds are not numerically optimized.

A bstract It has recently been argued that half degrees of freedom could emerge in Lorentz and parity invariant field theories, using a non-linear Proca field theory dubbed Proca-Nuevo as a specific example. We provide two proofs, using the Lagrangian and Hamiltonian pictures, that the theory possesses a pair of second class constraints, leaving D − 1 degrees of freedom in D spacetime dimensions, as befits a consistent Proca model. Our proofs are explicit and straightforward in two dimensions and we discuss how they generalize to an arbitrary number of dimensions. We also clarify why local Lorentz and parity invariant field theories cannot hold half degrees of freedom.

The vertical profile of air temperatures in subarctic regions is difficult to quantify, especially in areas with mountainous terrain subject to strong and lasting inversion events. Relying on observational data is not possible in most places due to sparse weather stations. To address this gap, we use reanalysis data to produce a model of the inversion strength. This model uses a single downscaled atmospheric column from reanalysis data and is calibrated with five weather stations close to Dawson City, Yukon, situated at various elevations. It is shown to perform better than bare reanalysis products and its parameters take into account the observed long-term decrease in frequency, strength, and depth of inversions since 1948, departing from the pattern of elevation-dependent warming found in lower latitude mountain regions. Once calibrated, the model only relies on global reanalysis data and hence can be applied in the vicinity of the calibration site, even where no observational data are available. Producing reliable time series for air temperature in complex terrain where inversions are strong and frequent is essential in modelling permafrost and understanding its future evolution. This model uses ever-improving physically based data, making it future-proof and versatile in its regional applications.

In the absence of a theory of everything, modern physicists need to rely on other predictive tools and turned to Effective Field Theories (EFTs) in a number of fields, including but not limited to statistical mechanics, condensed matter, particle physics, cosmology and gravity. The coefficients of an EFT can be constrained with high precision by experiments, which can involve high-energy particle colliders for instance but are generally left free from the theoretical point of view. The focus of this thesis is to use various consistency criteria to get theoretical constraints on the low-energy coefficients of EFTs. In particular, we construct a new model of massive spin-1 field by requiring that the theory is free of any ghostly degree of freedom. We then study its cosmological perturbations and ask that all propagating modes are stable and subluminal, reducing the space of viable cosmological solutions. Finally, we implement a method to get 'causality bounds', which are obtained by requiring infrared causality. This is imposed by forbidding any resolvable time advance in the EFT. We derive such 'causality bounds' for shift-symmetric and Galileon scalar EFTs, before turning to gauge-symmetric vector fields. We prove that our causality bounds can be competitive with positivity bounds and can even be used in scenarios that are out of reach of the positivity approach. The result of this thesis, by exploring several consistency criteria, is to provide compact causality bounds for low-energy EFT coefficients, in addition to constraints coming from the absence of ghosts, stability and cosmological viability.

I introduce (Extended) Proca-Nuevo, a non-linear theory of a massive spin-1 field enjoying a non-linearly realized constraint. I will provide a covariantization scheme that allows for consistent, ghost-free cosmological solutions, describing the correct number of dynamical variables in the presence of perfect fluid matter. I will finally exhibit explicit hot Big Bang solutions featuring a late-time self-accelerating epoch, where all the stability and subluminality conditions are satisfied and where gravitational waves behave precisely as in General Relativity.

We propose a new class of Proca interactions that enjoy a non-trivial constraint and hence propagates the correct number of degrees of freedom for a healthy massive spin-1 field. We show that the scattering amplitudes always differ from those of the Generalized Proca. This implies that the new class of interactions proposed here are genuinely different from the Generalized Proca and there can be no local field redefinitions between the two. In curved spacetime, massive gravity is the natural covariantization but we show how other classes of covariantizations can be considered.

Physical principles such as unitarity, causality, and locality can constrain the space of consistent effective field theories (EFTs) by imposing two-sided bounds on the allowed values of Wilson coefficients. In this paper, we consider the bounds that arise from the requirement of low-energy causality alone, without appealing to any assumptions about UV physics. We focus on shift-symmetric theories, and consider bounds that arise from the propagation around both a homogeneous and a spherically-symmetric background. We find that low-energy causality, namely the requirement that there are no resolvable time advances within the regime of validity of the EFT, produces two-sided bounds in agreement with compact positivity constraints previously obtained from \\(2 \\rightarrow 2\\) scattering amplitude dispersion relations using full crossing symmetry.

It has recently been argued that half degrees of freedom could emerge in Lorentz and parity invariant field theories, using a non-linear Proca field theory dubbed Proca-Nuevo as a specific example. We provide two proofs, using the Lagrangian and Hamiltonian pictures, that the theory possesses a pair of second class constraints, leaving \\(D-1\\) degrees of freedom in \\(D\\) spacetime dimensions, as befits a consistent Proca model. Our proofs are explicit and straightforward in two dimensions and we discuss how they generalize to an arbitrary number of dimensions. We also clarify why local Lorentz and parity invariant field theories cannot hold half degrees of freedom.

We introduce a family of tensor quantum-mechanical models based on irreducible rank-\\(3\\) representations of \\(\\mathrm{Sp}(N)\\). In contrast to irreducible tensor models with \\(\\mathrm{O}(N)\\) symmetry, the fermionic tetrahedral interaction does not vanish and can therefore support a melonic large \\(N\\) limit. The strongly-coupled regime has a very analogous structure as in the complex SYK model or in \\(\\mathrm{U}(N)\\times\\mathrm{O}(N)\\times\\mathrm{U}(N)\\) tensor quantum mechanics, the main difference being that the states are now singlets under \\(\\mathrm{Sp}(N)\\). We introduce character formulas that enumerate such singlets as a function of \\(N\\), and compute their first values. We conclude with an explicit numerical diagonalization of the Hamiltonian in two simple examples: the symmetric model at \\(N=1\\), and the antisymmetric traceless model at \\(N=3\\).

Proca-Nuevo is a non-linear theory of a massive spin-1 field which enjoys a non-linearly realized constraint that distinguishes it among other generalized vector models. We show that the theory may be extended by the addition of operators of the Generalized Proca class without spoiling the primary constraint that is necessary for consistency, allowing to interpolate between Generalized Proca operators and Proca-Nuevo ones. The constraint is maintained on flat spacetime and on any fixed curved background. Upon mixing extended Proca-Nuevo dynamically with gravity, we show that the constraint gets broken in a Planck scale suppressed way. We further prove that the theory may be covariantized in models that allow for consistent and ghost-free cosmological solutions. We study the models in the presence of perfect fluid matter, and show that they describe the correct number of dynamical variables and derive their dispersion relations and stability criteria. We also exhibit, in a specific set-up, explicit hot Big Bang solutions featuring a late-time self-accelerating epoch, and which are such that all the stability and subluminality conditions are satisfied and where gravitational waves behave precisely as in General Relativity.