Fermion Determinants: Some Recent Analytic Results

The use of known analytic results for the continuum fermion determinants in QCD and QED as benchmarks for zero lattice spacing extrapolations of lattice fermion determinants is proposed. Specifically, they can be used as a check on the universality hypothesis relating the continuum limits of the na\"{\i}ve, staggered and Wilson fermion determinants.Comment: 8th Workshop on Non-Perturbative QCD, 7-11 June 2004, Pari

Comment on `Hawking radiation from fluctuating black holes'

Takahashi & Soda (2010 Class. Quantum Grav. v27 p175008, arXiv:1005.0286) have recently considered the effect (at lowest non-trivial order) of dynamical, quantized gravitational fluctuations on the spectrum of scalar Hawking radiation from a collapsing Schwarzschild black hole. However, due to an unfortunate choice of gauge, the dominant (even divergent) contribution to the coefficient of the spectrum correction that they identify is a pure gauge artifact. I summarize the logic of their calculation, comment on the divergences encountered in its course and comment on how they could be eliminated, and thus the calculation be completed.Comment: 12 pages, 1 fig; feynmp, amsref

Perturbative and nonperturbative correspondences between compact and non-compact sigma-models

Compact (ferro- and antiferromagnetic) sigma-models and noncompact (hyperbolic) sigma-models are compared in a lattice formulation in dimensions $d \geq 2$. While the ferro- and antiferromagnetic models are essentially equivalent, the qualitative difference to the noncompact models is highlighted. The perturbative and the large $N$ expansions are studied in both types of models and are argued to be asymptotic expansions on a finite lattice. An exact correspondence between the expansion coefficients of the compact and the noncompact models is established, for both expansions, valid to all orders on a finite lattice. The perturbative one involves flipping the sign of the coupling and remains valid in the termwise infinite volume limit. The large $N$ correspondence concerns the functional dependence on the free propagator and holds directly only in finite volume

On the Structure of the Observable Algebra of QCD on the Lattice

The structure of the observable algebra ${\mathfrak O}_{\Lambda}$ of lattice QCD in the Hamiltonian approach is investigated. As was shown earlier, ${\mathfrak O}_{\Lambda}$ is isomorphic to the tensor product of a gluonic $C^{*}$-subalgebra, built from gauge fields and a hadronic subalgebra constructed from gauge invariant combinations of quark fields. The gluonic component is isomorphic to a standard CCR algebra over the group manifold SU(3). The structure of the hadronic part, as presented in terms of a number of generators and relations, is studied in detail. It is shown that its irreducible representations are classified by triality. Using this, it is proved that the hadronic algebra is isomorphic to the commutant of the triality operator in the enveloping algebra of the Lie super algebra ${\rm sl(1/n)}$ (factorized by a certain ideal).Comment: 33 page

Involution and Constrained Dynamics I: The Dirac Approach

We study the theory of systems with constraints from the point of view of the formal theory of partial differential equations. For finite-dimensional systems we show that the Dirac algorithm completes the equations of motion to an involutive system. We discuss the implications of this identification for field theories and argue that the involution analysis is more general and flexible than the Dirac approach. We also derive intrinsic expressions for the number of degrees of freedom.Comment: 28 pages, latex, no figure

Fermion Determinants

The current status of bounds on and limits of fermion determinants in two, three and four dimensions in QED and QCD is reviewed. A new lower bound on the two-dimensional QED determinant is derived. An outline of the demonstration of the continuity of this determinant at zero mass when the background magnetic field flux is zero is also given.Comment: 10 page

Isoform-specific, Semi-quantitative Determination of Highly Homologous Protein Levels via CRISPR-Cas9-mediated HiBiT Tagging.

Many protein families consist of multiple highly homologous proteins, whether they are encoded by different genes or originating from the same genomic location. Predominance of certain isoforms has been linked to various pathological conditions, such as cancer. Detection and relative quantification of protein isoforms in research are commonly done via immunoblotting, immunohistochemistry, or immunofluorescence, where antibodies against an isoform-specific epitope of particular family members are used. However, isoform-specific antibodies are not always available, making it impossible to decipher isoform-specific protein expression patterns. Here, we describe the insertion of the versatile 11 amino acid HiBiT tag into the genomic location of the protein of interest. This tag was developed and is distributed by Promega (Fitchburg, WI, USA). This protocol describes precise and specific protein expression analysis of highly homologous proteins through expression of the HiBiT tag, enabling protein expression quantification when specific antibodies are missing. Protein expression can be analyzed through traditional methods such as western blotting or immunofluorescence, and also in a luciferase binary reporter system, allowing for reliable and fast relative expression quantification using a plate reader. Graphical overview

Fifth-order two-quantum absorptive two-dimensional electronic spectroscopy of CdSe quantum dots

Two-quantum variants of two-dimensional electronic spectroscopy (2DES) have previously been used to characterize multi-exciton interactions in molecules and semiconductor nanostructures though many implementations are limited by phasing procedures or non-resonant signals. We implement 2DES using phase-cycling to simultaneously measure one-quantum and two-quantum spectra in colloidal CdSe quantum dots. In the pump–probe geometry, fully absorptive spectra are automatically acquired by measuring the sum of the rephasing and nonrephasing signals. Fifth-order two-quantum spectroscopy allows for direct access to multi-exciton states that may be obscured in excited state absorption signals due to population relaxation or third-order two-quantum spectra due to the non-resonant response