WE CANONICALLY QUANTIZE (2+1)-DIMENSIONAL ELECTRODYNAMICS INCLUDING A HIGHER-DERIVATIVE CHERN-SIMONS TERM. THE EFFECTIVE THEORY DESCRIBES A STANDARD PHOTON AND AN ADDITIONAL DEGREE OF FREEDOM ASSOCIATED WITH A MASSIVE GHOST. WE FIND THE HAMILTONIAN AND THE ALGEBRA SATISFIED BY THE FIELD OPERATORS. THE THEORY IS CHARACTERIZED BY AN INDEFINITE METRIC IN THE HILBERT SPACE THAT BRINGS UP QUESTIONS ON CAUSALITY AND UNITARITY. WE STUDY BOTH OF THE LATTER FUNDAMENTAL PROPERTIES AND SHOW THAT MICROCAUSALITY AS WELL AS PERTURBATIVE UNITARITY UP TO ONE-LOOP ORDER ARE CONSERVED WHEN THE LEE-WICK PRESCRIPTION IS EMPLOYED.

WE CONSIDER DIFFEOMORPHISM VIOLATION, WHICH IS PARAMETRIZED BY NONDYNAMICAL BACKGROUND FIELDS OF THE GRAVITATIONAL STANDARD-MODEL EXTENSION, AND STUDY ITS EFFECTS ON THE TIME EVOLUTION OF THE UNIVERSE. OUR GOAL IS TO IDENTIFY BACKGROUND FIELD CONFIGURATIONS THAT IMPLY STAGES OF ACCELERATED EXPANSION WITHOUT EXOTIC FORMS OF MATTER AND RADIATION PRESENT. ALTHOUGH OUR APPROACH GIVES RISE TO A SET OF RESTRICTIVE CONDITIONS, CONFIGURATIONS ARE ENCOUNTERED THAT EXHIBIT THIS PROPERTY OR SHOW OTHER INTERESTING BEHAVIORS. THE FINDINGS OF OUR ARTICLE, WHICH IS AMONG THE FIRST TO APPLY THE STANDARD-MODEL EXTENSION TO A COSMOLOGICAL SETTING, PROVIDE AN INITIAL UNDERSTANDING OF HOW TO TECHNICALLY INCORPORATE BACKGROUND FIELDS INTO THE COSMOLOGICAL EVOLUTION EQUATIONS AND WHAT THEIR PHENOMENOLOGICAL IMPACT MAY BE.

THE CURRENT PAPER IS DEDICATED TO DEVELOPING A (3+1) DECOMPOSITION FOR THE MINIMAL GRAVITATIONAL STANDARD-MODEL EXTENSION. OUR SETTING IS EXPLICIT DIFFEOMORPHISM VIOLATION AND WE FOCUS ON THE BACKGROUND FIELDS KNOWN IN THE LITERATURE AS U AND S??. THE HAMILTONIAN FORMALISM IS DEVELOPED FOR THESE CONTRIBUTIONS, WHICH AMOUNTS TO DERIVING MODIFIED HAMILTONIAN AND MOMENTUM CONSTRAINTS. WE THEN STUDY THE CONNECTION BETWEEN THESE MODIFIED CONSTRAINTS AND THE MODIFIED EINSTEIN EQUATIONS. IMPLICATIONS ARE DRAWN ON THE FORM OF THE BACKGROUND FIELDS TO GUARANTEE THE INTERNAL CONSISTENCY OF THE CORRESPONDING MODIFIED-GRAVITY THEORIES. IN THE COURSE OF OUR ANALYSIS, WE OBTAIN A SET OF CONSISTENCY REQUIREMENTS FOR U AND CERTAIN SECTORS OF S??. WE ARGUE THAT THE CONSTRAINT STRUCTURE REMAINS UNTOUCHED WHEN THESE CONDITIONS ARE SATISFIED. OUR RESULTS SHED LIGHT ON EXPLICIT VIOLATIONS OF DIFFEOMORPHISM INVARIANCE AND LOCAL LORENTZ INVARIANCE IN GRAVITY. THEY MAY TURN OUT TO BE VALUABLE FOR DEVELOPING A BETTER UNDERSTANDING OF EFFECTIVE MODIFIED-GRAVITY THEORIES.

THE ISSUE OF LORENTZ FINE-TUNING IN EFFECTIVE THEORIES CONTAINING HIGHER-ORDER OPERATORS IS STUDIED. TO THIS END, WE FOCUS ON THE MYERS?POSPELOV EXTENSION OF QED WITH DIMENSION-FIVE OPERATORS IN THE PHOTON SECTOR AND STANDARD FERMIONS. WE COMPUTE THE FERMION SELF-ENERGY AT ONE-LOOP ORDER CONSIDERING ITS EVEN AND ODD CPT CONTRIBUTIONS. IN THE EVEN SECTOR WE FIND SMALL RADIATIVE CORRECTIONS TO THE USUAL PARAMETERS OF QED WHICH ALSO TURN TO BE FINITE. IN THE ODD SECTOR THE AXIAL OPERATOR IS SHOWN TO CONTAIN UNSUPPRESSED EFFECTS OF LORENTZ VIOLATION LEADING TO A POSSIBLE FINE-TUNING. WE USE DIMENSIONAL REGULARIZATION TO DEAL WITH THE DIVERGENCIES AND A GENERIC PREFERRED FOUR-VECTOR. TAKING THE FIRST STEPS IN THE RENORMALIZATION PROCEDURE FOR LORENTZ VIOLATING THEORIES WE ARRIVE TO ACCEPTABLE SMALL CORRECTIONS ALLOWING TO SET THE BOUND .

EFFECTIVE FIELD THEORY HAS SHOWN TO BE A POWERFUL METHOD IN SEARCHING FOR QUANTUM GRAVITY EFFECTS AND IN PARTICULAR FOR CPT AND LORENTZ SYMMETRY VIOLATION. IN THIS WORK WE STUDY AN EFFECTIVE FIELD THEORY WITH HIGHER-ORDER LORENTZ VIOLATION, SPECIFICALLY WE CONSIDER A MODIFIED MODEL WITH SCALARS AND MODIFIED FERMIONS INTERACTING VIA THE YUKAWA COUPLING. WE STUDY ITS RENORMALIZATION PROPERTIES, THAT IS, ITS RADIATIVE CORRECTIONS AND RENORMALIZATION CONDITIONS IN THE LIGHT OF THE REQUIREMENTS OF HAVING A FINITE AND UNITARY S-MATRIX.

WE CONSIDER THE TWO-POINT FUNCTION OF THE GAUGE FIELD IN LORENTZ-BREAKING THEORIES WITH HIGHER-DERIVATIVE EXTENSION OF THE DIRAC LAGRANGIAN. WE SHOW THAT THE CARROLL-FIELD-JACKIW TERM NATURALLY ARISES IN THIS THEORY AS A QUANTUM CORRECTION BEING PERFECTLY FINITE AND THUS DISPLAYING NO AMBIGUITIES. ALSO, THE FINITENESS OF THIS TERM AT THE LOW ENERGY LIMIT AND THE ABSENCE OF LARGE LORENTZ VIOLATING CORRECTIONS ALLOWS TO AVOID THE FINE-TUNING PROBLEM.

IN THIS WORK, IN THE LIGHT OF THE DEVELOPMENTS FOR INDEFINITE METRIC THEORIES MADE BY LEE AND WICK, WE STUDY PERTURBATIVE UNITARITY IN A LORENTZ-INVARIANCE VIOLATING QED MODEL WITH HIGHER-ORDER OPERATORS. WE SHOW THAT BY FOLLOWING THE LEE-WICK PRESCRIPTION IT IS POSSIBLE TO PRESERVE UNITARITY IN THE MODEL AT ONE-LOOP ORDER IN THE COUPLING

WE STUDY THE FERMIONIC SECTOR OF THE MYERS AND POSPELOV THEORY WITH A GENERAL BACKGROUND N. THE SPACELIKE CASE WITHOUT TEMPORAL COMPONENT IS WELL DEFINED AND NO NEW INGREDIENTS CAME ABOUT, APART FROM THE EXPLICIT LORENTZ INVARIANCE VIOLATION. THE LIGHTLIKE CASE IS ILL DEFINED AND PHYSICALLY DISCARDED. HOWEVER, THE OTHER CASE WHERE A NONVANISHING TEMPORAL COMPONENT OF THE BACKGROUND IS PRESENT, THE THEORY IS PHYSICALLY CONSISTENT. WE SHOW THAT NEW MODES APPEAR AS A CONSEQUENCE OF HIGHER TIME DERIVATIVES. WE QUANTIZE THE TIMELIKE THEORY AND CALCULATE THE MICROCAUSALITY VIOLATION WHICH TURNS OUT TO OCCUR NEAR THE LIGHT CONE.

WE STUDY THE DYNAMICS OF A MODIFIED-GRAVITY THEORY, WHICH IS SUPPLEMENTED BY AN EXTENDED GIBBONSHAWKING-YORK BOUNDARY TERM AND INCORPORATES DIFFEOMORPHISM VIOLATION THROUGH NONDYNAMICAL BACKGROUND FIELDS DENOTED AS U AND S?? IN THE LITERATURE. AN ADM DECOMPOSITION ALLOWS US TO PROJECT THE MODIFIED EINSTEIN EQUATIONS INTO PURELY SPACELIKE HYPERSURFACES, WHICH IMPLIES THE FIELD EQUATIONS FOR THE INDUCED DYNAMICAL THREE-METRIC. WE ALSO OBTAIN THE HAMILTON-JACOBI EQUATIONS OF MOTION FOR THE CANONICAL VARIABLES OF THE THEORY BASED ON ITS HAMILTONIAN, WHICH WAS DERIVED IN A PREVIOUS WORK. THE COMPUTATIONS SHOW THAT THE DYNAMICAL FIELD EQUATIONS OBTAINED FROM THE LAGRANGIAN AND HAMILTONIAN APPROACHES ARE CONSISTENT WITH EACH OTHER. CONNECTIONS TO BRANS-DICKE THEORY AND GHOST-FREE MASSIVE GRAVITY ARE ESTABLISHED.

WE STUDY A GENERALIZATION OF THE PAIS-UHLENBECK OSCILLATOR FOR FERMIONIC VARIABLES. NEXT, WE CONSIDER AN ENSEMBLE OF THESE OSCILLATORS AND WE IDENTIFY A PARTICULAR CASE OF THE MYERS?POSPELOV MODEL WHICH IS RELEVANT FOR EFFECTIVE THEORIES OF QUANTUM GRAVITY. FINALLY, BY TAKING ADVANTAGE OF THIS CONNECTION, WE ANALYZE, FOR THIS MODEL, UNITARITY AT ONE LOOP ORDER IN THE LOW ENERGY REGIME WHERE NO GHOST STATES CAN BE CREATED ON-SHELL. THIS ENERGY REGIME IS THE RELEVANT ONE WHEN WE CONSIDER THE MYERS?POSPELOV MODEL AS A TRUE EFFECTIVE THEORY COMING FROM A NEW SPACE-TIME STRUCTURE.

A NUMERICAL METHOD BASED ON ARTIFICIAL NEURAL NETWORKS IS USED TO SOLVE THE INVERSE SCHRÖDINGER EQUATION FOR A MULTI-PARAMETER CLASS OF POTENTIALS. FIRST, THE FINITE ELEMENT METHOD WAS USED TO SOLVE REPEATEDLY THE DIRECT PROBLEM FOR DIFFERENT PARAMETRIZATIONS OF THE CHOSEN POTENTIAL FUNCTION. THEN, USING THE ATTAINABLE EIGENVALUES AS A TRAINING SET OF THE DIRECT RADIAL BASIS NEURAL NETWORK A MAP OF NEW EIGENVALUES WAS OBTAINED. THIS RELATIONSHIP WAS LATER INVERTED AND REFINED BY TRAINING AN INVERSE RADIAL BASIS NEURAL NETWORK, ALLOWING THE CALCULATION OF THE UNKNOWN PARAMETERS AND THEREFORE ESTIMATING THE POTENTIAL FUNCTION. THREE NUMERICAL EXAMPLES ARE PRESENTED IN ORDER TO PROVE THE EFFECTIVENESS OF THE METHOD. THE RESULTS SHOW THAT THE METHOD PROPOSED HAS THE ADVANTAGE TO USE LESS COMPUTATIONAL RESOURCES WITHOUT A SIGNIFICANT ACCURACY LOSS.

A CLASS OF EFFECTIVE FIELD THEORY CALLED DELTA-THEORY, WHICH IMPROVES ULTRAVIOLET DIVERGENCES IN QUANTUM FIELD THEORY, IS CONSIDERED. WE FOCUS ON A SCALAR MODEL WITH A QUARTIC SELF-INTERACTION TERM AND CONSTRUCT THE DELTA THEORY BY APPLYING THE SO-CALLED DELTA PRESCRIPTION. WE QUANTIZE THE THEORY USING FIELD VARIABLES THAT DIAGONALIZE THE LAGRANGIAN, WHICH INCLUDE A STANDARD SCALAR FIELD AND A GHOST OR NEGATIVE NORM STATE. AS WELL KNOWN, THE INDEFINITE METRIC MAY LEAD TO THE LOSS OF UNITARY OF THE S-MATRIX. WE STUDY THE OPTICAL THEOREM AND CHECK THE VALIDITY OF THE CUTTING EQUATIONS FOR THREE PROCESSES AT ONE-LOOP ORDER, AND FOUND SUPPRESSED VIOLATIONS OF UNITARITY IN THE DELTA COUPLING PARAMETER OF THE ORDER OF ?4.

WE INVESTIGATE THE PRESERVATION OF UNITARITY IN A LORENTZ AND CPT-VIOLATING QED MODEL CONTAINING HIGHER-ORDER OPERATORS. IN PARTICULAR, WE CONSIDER MODIFICATIONS IN THE FERMION SECTOR WITH DIMENSION-FIVE OPERATORS. THE HIGHER-ORDER OPERATORS LEAD TO AN INDEFINITE METRIC AND A PSEUDO-UNITARITY RELATION FOR THE S-MATRIX. HOWEVER, WE SHOW THAT THE PSEUDO-UNITARITY CONDITION CAN BE PROMOTED TO A GENUINE UNITARITY RELATION BY (I) RESTRICTING THE ENERGIES TO THE EFFECTIVE REGION FAR BELOW THE PLANCK MASS AND (II) CONSIDERING STABLE PARTICLES TO HAVE A POSITIVE METRIC. IN THE CONTEXT OF THE OPTICAL THEOREM, WE FOCUS ON THE ONE-LOOP BHABHA AND COMPTON SCATTERING PROCESSES. WE SHOW THAT NO GHOST STATES GET PROPAGATED THROUGH THE CUTS, THUS SATISFYING THE UNITARITY CONDITION. FURTHER, WE SHOW THAT DISCONTINUITIES OF PROPAGATORS ARE EQUIVALENT TO REPLACING PHYSICAL DIRAC FUNCTIONALS IN THE CUTTING EQUATION. THE PHYSICAL DIRAC FUNCTIONALS ARE DEFINED TO SELECT ONLY MODE SOLUTIONS OF STABLE PARTICLES. THE PROVIDED EXTENSION OF THE CUTKOSKY RULE MAY BE HELPFUL FOR ANALYZING PERTURBATIVE UNITARITY IN HIGHER-ORDER DIAGRAMS.

WE STUDY PERTURBATIVE UNITARITY IN THE SCALAR SECTOR OF THE MYERS-POSPELOV MODEL. THE MODEL INTRODUCES A PREFERRED FOUR-VECTOR N WHICH BREAKS LORENTZ SYMMETRY AND COUPLES TO A FIVE-DIMENSION OPERATOR. WHEN THE PREFERRED FOUR-VECTOR IS CHOSEN IN THE PURE TIMELIKE OR LIGHTLIKE DIRECTION, THE MODEL BECOMES A HIGHER TIME DERIVATIVE THEORY, LEADING TO A CUBIC DISPERSION RELATION. TWO OF THE POLES ARE SHOWN TO BE PERTURBATIVELY CONNECTED TO THE STANDARD ONES, WHILE A THIRD POLE, WHICH WE CALL THE LEE-WICK-LIKE POLE, IS ASSOCIATED TO A NEGATIVE METRIC IN HILBERT SPACE, THREATENING THE PRESERVATION OF UNITARITY. THE PURE SPACELIKE CASE IS A NORMAL THEORY IN THE SENSE THAT IT HAS ONLY TWO SOLUTIONS, BOTH BEING SMALL PERTURBATIONS OVER THE STANDARD ONES. WE ANALYZE PERTURBATIVE UNITARITY FOR PURELY SPACELIKE AND TIMELIKE CASES USING THE OPTICAL THEOREM AND CONSIDERING A QUARTIC SELF-INTERACTION TERM. BY COMPUTING DISCONTINUITIES IN THE LOOP DIAGRAM, WE ARRIVE AT A PINCHING CONDITION WHICH DETERMINES THE PROPAGATION OF PARTICLES AND LEE-WICK-LIKE PARTICLES THROUGH THE CUT. WE FIND THAT THE CONTRIBUTION FOR LEE-WICK-LIKE PARTICLES VANISHES FOR ANY EXTERNAL MOMENTA, LEAVING ONLY THE CONTRIBUTION OF PARTICLES, THUS PRESERVING ONE-LOOP UNITARITY IN BOTH CASES.

THE POSSIBILITY THAT FUNDAMENTAL DISCRETENESS IMPLICIT IN A QUANTUM GRAVITY THEORY MAY ACT AS A NATURAL REGULATOR FOR ULTRAVIOLET SINGULARITIES ARISING IN QUANTUM FIELD THEORY HAS BEEN INTENSIVELY STUDIED. HERE, ALONG THE SAME EXPECTATIONS, WE INVESTIGATE WHETHER A NONSTANDARD REPRESENTATION CALLED POLYMER REPRESENTATION CAN SMOOTH AWAY THE LARGE AMOUNT OF NEGATIVE ENERGY THAT AFFLICTS THE HAMILTONIANS OF HIGHER-ORDER TIME DERIVATIVE THEORIES, RENDERING THE THEORY UNSTABLE WHEN INTERACTIONS COME INTO PLAY. WE FOCUS ON THE FOURTH-ORDER PAIS-UHLENBECK MODEL WHICH CAN BE REEXPRESSED AS THE SUM OF TWO DECOUPLED HARMONIC OSCILLATORS ONE PRODUCING POSITIVE ENERGY AND THE OTHER NEGATIVE ENERGY. AS EXPECTED, THE SCHRODINGER QUANTIZATION OF SUCH MODEL LEADS TO THE STABILITY PROBLEM OR TO NEGATIVE NORM STATES CALLED GHOSTS. WITHIN THE FRAMEWORK OF POLYMER QUANTIZATION WE SHOW THE EXISTENCE OF NEW REGIONS WHERE THE HAMILTONIAN CAN BE DEFINED WELL BOUNDED FROM BELOW.

WE CONSIDER THE HIGHER-DERIVATIVE LORENTZ-BREAKING EXTENSION OF QED, WHERE THE NEW TERMS ARE THE MYERS-POSPELOV-LIKE ONES IN GAUGE AND SPINOR SECTORS, AND THE HIGHER?DERIVATIVE CARROLL-FIELD-JACKIW TERM. FOR THIS THEORY, WE STUDY ITS TREE-LEVEL DYNAMICS, DISCUSS THE DISPERSION RELATION, AND PRESENT ONE MORE SCHEME FOR ITS PERTURBATIVE GENERATION, INCLUDING THE FINITE-TEMPERATURE CASE. ALSO, WE DEVELOP A METHOD TO STUDY PERTURBATIVE UNITARITY BASED ON CONSISTENT ROTATION OF THE THEORY TO EUCLIDEAN SPACE. WE USE THIS METHOD TO VERIFY EXPLICITLY THAT FOR SPECIAL CHOICES OF THE LORENTZ-BREAKING VECTOR THE UNITARITY IS PRESERVED AT THE ONE-LOOP LEVEL, EVEN IN THE PRESENCE OF HIGHER TIME DERIVATIVES.

WE STUDY THE POSSIBLE EFFECTS OF LARGE LORENTZ VIOLATIONS THAT CAN APPEAR IN THE EFFECTIVE MODELS IN WHICH THE LORENTZ SYMMETRY BREAKDOWN IS PERFORMED WITH HIGHER-ORDER OPERATORS. FOR THIS WE CONSIDER THE MYERS AND POSPELOV EXTENSION OF QED WITH DIMENSION-FIVE OPERATORS IN THE PHOTON SECTOR AND STANDARD FERMIONS. WE FOCUS ON THE FERMION SELF-ENERGY AT ONE-LOOP ORDER AND FIND SMALL AND FINITE RADIATIVE CORRECTIONS IN THE EVEN CPT SECTOR. IN THE ODD CPT SECTOR A LOWER DIMENSIONAL OPERATOR IS GENERATED WHICH CONTAINS UNSUPPRESSED EFFECTS OF LORENTZ VIOLATION LEADING TO A POSSIBLE FINE-TUNING. FOR THE CALCULATION OF DIVERGENT DIAGRAMS WE USE DIMENSIONAL REGULARIZATION AND CONSIDER AN ARBITRARY BACKGROUND FOUR-VECTOR.

THE RENORMALIZATION IN A LORENTZ-BREAKING SCALAR-SPINOR HIGHER-DERIVATIVE MODEL INVOLVING ?4 SELF-INTERACTION AND THE YUKAWA-LIKE COUPLING IS STUDIED. WE EXPLICITLY DE-MONSTRATE THAT THE CONVERGENCE IS IMPROVED IN COMPARISON WITH THE USUAL SCALAR-SPINOR MODEL, SO, THE THEORY IS SUPER-RENORMALIZABLE, WITH NO DIVERGENCES BEYOND FOUR LOOPS. WE COMPUTE THE ONE-LOOP CORRECTIONS TO THE PROPAGATORS FOR THE SCALAR AND FERMIONIC FIELDS AND SHOW THAT IN THE PRESENCE OF HIGHER-ORDER LORENTZ INVARIANCE VIOLATION, THE POLES THAT DOMINATE THE PHYSICAL THEORY, ARE DRIVEN AWAY FROM THE STANDARD ON-SHELL POLE MASS DUE TO RADIATIVELY INDUCED LOWER DIMENSIONAL OPERATORS. THE NEW OPERATORS CHANGE THE STANDARD GAMMA-MATRIX STRUCTURE OF THE TWO-POINT FUNCTIONS, INTRODUCE LARGE LORENTZ-BREAKING CORRECTIONS AND LEAD TO MODIFICATIONS IN THE RENORMALIZATION CONDITIONS OF THE THEORY. WE FOUND THE PHYSICAL POLE MASS IN EACH SECTOR OF OUR MODEL.

WE PROVIDE THE FIRST STEP TOWARDS RENORMALIZATION IN A NONMINIMAL LORENTZ-VIOLATING MODEL CONSISTING OF NORMAL SCALARS AND MODIFIED FERMIONS WITH MASS DIMENSION FIVE OPERATORS. WE COMPUTE THE RADIATIVE CORRECTIONS CORRESPONDING TO THE SCALAR SELF-ENERGY, AND WE SHOW THAT SOME DIVERGENCIES ARE IMPROVED AND IN THE SCALAR SECTOR THEY ARE FINITE. THE POLE MASS OF THE SCALAR TWO-POINT FUNCTION IS FOUND AND SHOWN TO LEAD TO MODIFICATIONS OF ASYMPTOTIC STATES.