Clifford Algebras in Symplectic Geometry and Quantum Mechanics

The necessary appearance of Clifford algebras in the quantum description of fermions has prompted us to re-examine the fundamental role played by the quaternion Clifford algebra, C(0,2). This algebra is essentially the geometric algebra describing the rotational properties of space. Hidden within this algebra are symplectic structures with Heisenberg algebras at their core. This algebra also enables us to define a Poisson algebra of all homogeneous quadratic polynomials on a two-dimensional sub-space, Fa of the Euclidean three-space. This enables us to construct a Poisson Clifford algebra, H(F), of a finite dimensional phase space which will carry the dynamics. The quantum dynamics appears as a realization of H(F) in terms of a Clifford algebra consisting of Hermitian operators.Comment: 17 page

The Reconstruction Problem and Weak Quantum Values

Quantum Mechanical weak values are an interference effect measured by the cross-Wigner transform W({\phi},{\psi}) of the post-and preselected states, leading to a complex quasi-distribution {\rho}_{{\phi},{\psi}}(x,p) on phase space. We show that the knowledge of {\rho}_{{\phi},{\psi}}(z) and of one of the two functions {\phi},{\psi} unambiguously determines the other, thus generalizing a recent reconstruction result of Lundeen and his collaborators.Comment: To appear in J.Phys.: Math. Theo

Symplectically Covariant Schr\"{o}dinger Equation in Phase Space

A classical theorem of Stone and von Neumann says that the Schr\"{o}dinger representation is, up to unitary equivalences, the only irreducible representation of the Heisenberg group on the Hilbert space of square-integrable functions on configuration space. Using the Wigner-Moyal transform we construct an irreducible representation of the Heisenberg group on a certain Hilbert space of square-integrable functions defined on phase space. This allows us to extend the usual Weyl calculus into a phase-space calculus and leads us to a quantum mechanics in phase space, equivalent to standard quantum mechanics. We also briefly discuss the extension of metaplectic operators to phase space and the probabilistic interpretation of the solutions of the phase space Schr\"{o}dinger equationComment: To appear in J Phys

Grounding Bohmian Mechanics in Weak Values and Bayesianism

Bohmian mechanics (BM) is a popular interpretation of quantum mechanics in which particles have real positions. The velocity of a point x in configuration space is defined as the standard probability current j(x) divided by the probability density P(x). However, this ``standard'' j is in fact only one of infinitely many that transform correctly and satisfy \dot P + \del . j=0. In this article I show that there is a unique j that can be determined experimentally as a weak value using techniques that would make sense to a classical physicist. Moreover, this operationally defined j equals the standard j, so, assuming \dot x = j/P, the possible Bohmian paths can also be determined experimentally from a large enough ensemble. Furthermore, this approach to deriving BM singles out x as the hidden variable, because (for example) the operationally defined momentum current is in general incompatible with the evolution of the momentum distribution. Finally I discuss how, in this setting, the usual quantum probabilities can be derived from a Bayesian standpoint, via the principle of indifference.Comment: 11 page

Evidence of exactness of the mean field theory in the nonextensive regime of long-range spin models

The q-state Potts model with long-range interactions that decay as 1/r^alpha subjected to an uniform magnetic field on d-dimensional lattices is analized for different values of q in the nonextensive regime (alpha between 0 and d). We also consider the two dimensional antiferromagnetic Ising model with the same type of interactions. The mean field solution and Monte Carlo calculations for the equations of state for these models are compared. We show that, using a derived scaling which properly describes the nonextensive thermodynamic behaviour, both types of calculations show an excellent agreement in all the cases here considered, except for alpha=d. These results allow us to extend to nonextensive magnetic models a previous conjecture which states that the mean field theory is exact for the Ising one.Comment: 10 pages, 4 figure

Changes in the Management of Patients having Radical Radiotherapy for Lung Cancer during the First Wave of the COVID-19 Pandemic in the UK.

AIMS: In response to the COVID-19 pandemic, guidelines on reduced fractionation for patients treated with curative-intent radiotherapy were published, aimed at reducing the number of hospital attendances and potential exposure of vulnerable patients to minimise the risk of COVID-19 infection. We describe the changes that took place in the management of patients with stage I-III lung cancer from April to October 2020. MATERIALS AND METHODS: Lung Radiotherapy during the COVID-19 Pandemic (COVID-RT Lung) is a prospective multicentre UK cohort study. The inclusion criteria were: patients with stage I-III lung cancer referred for and/or treated with radical radiotherapy between 2nd April and 2nd October 2020. Patients who had had a change in their management and those who continued with standard management were included. Data on demographics, COVID-19 diagnosis, diagnostic work-up, radiotherapy and systemic treatment were collected and reported as counts and percentages. Patient characteristics associated with a change in treatment were analysed using multivariable binary logistic regression. RESULTS: In total, 1553 patients were included (median age 72 years, 49% female); 93 (12%) had a change to their diagnostic investigation and 528 (34%) had a change to their treatment from their centre's standard of care as a result of the COVID-19 pandemic. Age ≥70 years, male gender and stage III disease were associated with a change in treatment on multivariable analysis. Patients who had their treatment changed had a median of 15 fractions of radiotherapy compared with a median of 20 fractions in those who did not have their treatment changed. Low rates of COVID-19 infection were seen during or after radiotherapy, with only 21 patients (1.4%) developing the disease. CONCLUSIONS: The COVID-19 pandemic resulted in changes to patient treatment in line with national recommendations. The main change was an increase in hypofractionation. Further work is ongoing to analyse the impact of these changes on patient outcomes

A formalism for steering with local quantum measurements

We develop a unified approach to classical, quantum and post-quantum steering. The framework is based on uncharacterised (black-box) parties performing quantum measurements on their share of a (possibly unphysical) quantum state, and its starting point is the characterisation of general no- signalling assemblages via non-positive local hidden-state models. By developing a connection to entanglement witnesses, this formalism allows for new definitions of families of assemblages, in particular via (i) non-decomposable positive maps and (ii) unextendible product bases. The former proves to be useful for constructing post-quantum assemblages with the built-in feature of yielding only quantum correlations in Bell experiments, while the latter always gives certifiably post-quantum assemblages. Finally, our framework is equipped with an inherent quantifier of post-quantum steering, which we call the negativity of post-quantum steering. We postulate that post-quantum steering should not increase under one-way quantum operations from the steered parties to the steering parties, and we show that, in this sense, the negativity of post-quantum steering is a convex post-quantum-steering monotone

The RHO-1 RhoGTPase Modulates Fertility and Multiple Behaviors in Adult C. elegans

The Rho family of small GTPases are essential during early embryonic development making it difficult to study their functions in adult animals. Using inducible transgenes expressing either a constitutively active version of the single C. elegans Rho ortholog, RHO-1, or an inhibitor of endogenous Rho (C3 transferase), we demonstrate multiple defects caused by altering Rho signaling in adult C. elegans. Changes in RHO-1 signaling in cholinergic neurons affected locomotion, pharyngeal pumping and fecundity. Changes in RHO-1 signaling outside the cholinergic neurons resulted in defective defecation, ovulation, and changes in C. elegans body morphology. Finally both increased and decreased RHO-1 signaling in adults resulted in death within hours. The multiple post-developmental roles for Rho in C. elegans demonstrate that RhoA signaling pathways continue to be used post-developmentally and the resulting phenotypes provide an opportunity to further study post-developmental Rho signaling pathways using genetic screens

The T cell differentiation landscape is shaped by tumour mutations in lung cancer

Tumour mutational burden (TMB) predicts immunotherapy outcome in non-small cell lung cancer (NSCLC), consistent with immune recognition of tumour neoantigens. However, persistent antigen exposure is detrimental for T cell function. How TMB affects CD4 and CD8 T cell differentiation in untreated tumours and whether this affects patient outcomes is unknown. Here, we paired high-dimensional flow cytometry, exome, single-cell and bulk RNA sequencing from patients with resected, untreated NSCLC to examine these relationships. TMB was associated with compartment-wide T cell differentiation skewing, characterized by loss of TCF7-expressing progenitor-like CD4 T cells, and an increased abundance of dysfunctional CD8 and CD4 T cell subsets with strong phenotypic and transcriptional similarity to neoantigen-reactive CD8 T cells. A gene signature of redistribution from progenitor-like to dysfunctional states was associated with poor survival in lung and other cancer cohorts. Single-cell characterization of these populations informs potential strategies for therapeutic manipulation in NSCLC

Antibodies against endogenous retroviruses promote lung cancer immunotherapy

B cells are frequently found in the margins of solid tumours as organized follicles in ectopic lymphoid organs called tertiary lymphoid structures (TLS)1,2. Although TLS have been found to correlate with improved patient survival and response to immune checkpoint blockade (ICB), the underlying mechanisms of this association remain elusive1,2. Here we investigate lung-resident B cell responses in patients from the TRACERx 421 (Tracking Non-Small-Cell Lung Cancer Evolution Through Therapy) and other lung cancer cohorts, and in a recently established immunogenic mouse model for lung adenocarcinoma3. We find that both human and mouse lung adenocarcinomas elicit local germinal centre responses and tumour-binding antibodies, and further identify endogenous retrovirus (ERV) envelope glycoproteins as a dominant anti-tumour antibody target. ERV-targeting B cell responses are amplified by ICB in both humans and mice, and by targeted inhibition of KRAS(G12C) in the mouse model. ERV-reactive antibodies exert anti-tumour activity that extends survival in the mouse model, and ERV expression predicts the outcome of ICB in human lung adenocarcinoma. Finally, we find that effective immunotherapy in the mouse model requires CXCL13-dependent TLS formation. Conversely, therapeutic CXCL13 treatment potentiates anti-tumour immunity and synergizes with ICB. Our findings provide a possible mechanistic basis for the association of TLS with immunotherapy respons