A Rejoinder on Quaternionic Projective Representations

In a series of papers published in this Journal (J. Math. Phys.), a discussion was started on the significance of a new definition of projective representations in quaternionic Hilbert spaces. The present paper gives what we believe is a resolution of the semantic differences that had apparently tended to obscure the issues.Comment: AMStex, 6 Page

Alternative Descriptions in Quaternionic Quantum Mechanics

We characterize the quasianti-Hermitian quaternionic operators in QQM by means of their spectra; moreover, we state a necessary and sufficient condition for a set of quasianti-Hermitian quaternionic operators to be anti-Hermitian with respect to a uniquely defined positive scalar product in a infinite dimensional (right) quaternionic Hilbert space. According to such results we obtain two alternative descriptions of a quantum optical physical system, in the realm of quaternionic quantum mechanics, while no alternative can exist in complex quantum mechanics, and we discuss some differences between them.Comment: 16 page

Associations Between Financial Strain and Emotional Well-Being With Physiological Responses to Acute Mental Stress

OBJECTIVE: To investigate associations between financial strain and emotional wellbeing, health, and physiological responses to acute mental stress. METHODS: Participants were 542 healthy men and women aged 53-76y from the Whitehall II study divided into those who reported no (n = 316), some (n =135) or moderate/severe (n = 91) financial strain. Emotional wellbeing and self-reported health were assessed at baseline and 3 years later. Laboratory mental stress testing involved assessment of blood pressure (BP), heart rate, and lipid reactivity and recovery, and plasma interleukin 6 (IL-6) responses to challenging behavioral tasks. Analyses adjusted for objective financial status, age, sex, socioeconomic status (SES) and marital status. RESULTS: Financial strain was positively associated with more depressive symptoms, lower positive affect, greater loneliness, and lower optimism, self-esteem and sense of control, and with poorer self-reported physical health, mental health and sleep (all p <.001). Longitudinally, financial strain predicted poorer outcomes 3 years later, but associations were attenuated after baseline levels were taken into account. Financial strain was associated with reduced systolic and diastolic BP reactivity to acute stress (mean systolic BP increase 32.34 ± 15.2, 28.95 ± 13.1 and 27.26 ± 15.2 mmHg in the none, some, and moderate/severe financial strain groups), but not with heart rate, IL-6 or lipid responses. CONCLUSIONS: Financial strain was correlated with a range of emotional and health-related outcomes independently of objective financial status. The diminished BP reactions to acute mental stress suggest that financial strain may contribute to dynamic chronic allostatic load

The role of infrared divergence for decoherence

Continuous and discrete superselection rules induced by the interaction with the environment are investigated for a class of exactly soluble Hamiltonian models. The environment is given by a Boson field. Stable superselection sectors emerge if and only if the low frequences dominate and the ground state of the Boson field disappears due to infrared divergence. The models allow uniform estimates of all transition matrix elements between different superselection sectors.Comment: 11 pages, extended and simplified proo

Continuous slice functional calculus in quaternionic Hilbert spaces

The aim of this work is to define a continuous functional calculus in quaternionic Hilbert spaces, starting from basic issues regarding the notion of spherical spectrum of a normal operator. As properties of the spherical spectrum suggest, the class of continuous functions to consider in this setting is the one of slice quaternionic functions. Slice functions generalize the concept of slice regular function, which comprises power series with quaternionic coefficients on one side and that can be seen as an effective generalization to quaternions of holomorphic functions of one complex variable. The notion of slice function allows to introduce suitable classes of real, complex and quaternionic $C^*$--algebras and to define, on each of these $C^*$--algebras, a functional calculus for quaternionic normal operators. In particular, we establish several versions of the spectral map theorem. Some of the results are proved also for unbounded operators. However, the mentioned continuous functional calculi are defined only for bounded normal operators. Some comments on the physical significance of our work are included.Comment: 71 pages, some references added. Accepted for publication in Reviews in Mathematical Physic

The legacy of redlining in the effect of foreclosures on Detroit residents’ self-rated health

Historical practices, such as housing discrimination in Detroit, have been shown to have lasting impacts on communities. Perhaps the most explicit example is the practice of redlining in the 1930s, whereby lenders outlined financially undesirable neighborhoods, populated by minority families, on maps and prevented residents from moving to better resourced neighborhoods. Awareness of historical housing discrimination may improve research assessing the impacts of current neighborhood characteristics on health. Using the Detroit Neighborhood Health Study (DNHS), we assessed the association between two-year changes in home foreclosure rates following the 2007–2008 Great Recession, and residents’ five-year self-rated health trajectories (2008–2013); and estimated the confounding bias introduced by ignoring historical redlining practices in the city. We used both ecological and multilevel models to make inference about person- and community-level processes. In a neighborhood-level linear regression adjusted for confounders (including percent redlined); a 10%-point slower foreclosure rate recovery was associated with an increase in prevalence of poor self-rated health of 0.31 (95% CI:−0.02 to 0.64). At the individual level, it was associated with a within-person increase in probability of poor health of 0.45 (95% CI:0.15–0.72). Removing redlining from the model biased the estimated effect upward to 0.38 (95% CI:0.07–0.69) and 0.56 (95% CI:0.21–0.84) in the neighborhood and individual-level models, respectively. Stratum-specific foreclosure recovery effects indicate stronger influence in neighborhoods with a greater proportion of residents identifying as white and a greater degree of historic redlining. These findings support earlier theory suggesting a historical influence of structural discrimination on the association between current neighborhood characteristics and health, and suggests that historical redlining specifically may increase vulnerability to contemporary neighborhood foreclosures. Community interventions should consider historical discrimination in conjunction with current place-based indicators to more equitably improve population health

The Possibility of Reconciling Quantum Mechanics with Classical Probability Theory

We describe a scheme for constructing quantum mechanics in which a quantum system is considered as a collection of open classical subsystems. This allows using the formal classical logic and classical probability theory in quantum mechanics. Our approach nevertheless allows completely reproducing the standard mathematical formalism of quantum mechanics and identifying its applicability limits. We especially attend to the quantum state reduction problem.Comment: Latex, 14 pages, 1 figur

On the realization of Symmetries in Quantum Mechanics

The aim of this paper is to give a simple, geometric proof of Wigner's theorem on the realization of symmetries in quantum mechanics that clarifies its relation to projective geometry. Although several proofs exist already, it seems that the relevance of Wigner's theorem is not fully appreciated in general. It is Wigner's theorem which allows the use of linear realizations of symmetries and therefore guarantees that, in the end, quantum theory stays a linear theory. In the present paper, we take a strictly geometrical point of view in order to prove this theorem. It becomes apparent that Wigner's theorem is nothing else but a corollary of the fundamental theorem of projective geometry. In this sense, the proof presented here is simple, transparent and therefore accessible even to elementary treatments in quantum mechanics.Comment: 8 page

The Geometric Phase and Ray Space Isometries

We study the behaviour of the geometric phase under isometries of the ray space. This leads to a better understanding of a theorem first proved by Wigner: isometries of the ray space can always be realised as projections of unitary or anti-unitary transformations on the Hilbert space. We suggest that the construction involved in Wigner's proof is best viewed as an use of the Pancharatnam connection to ``lift'' a ray space isometry to the Hilbert space.Comment: 17 pages, Latex file, no figures, To appear in Pramana J. Phy

Approach to equilibrium for a class of random quantum models of infinite range

We consider random generalizations of a quantum model of infinite range introduced by Emch and Radin. The generalization allows a neat extension from the class $l_1$ of absolutely summable lattice potentials to the optimal class $l_2$ of square summable potentials first considered by Khanin and Sinai and generalised by van Enter and van Hemmen. The approach to equilibrium in the case of a Gaussian distribution is proved to be faster than for a Bernoulli distribution for both short-range and long-range lattice potentials. While exponential decay to equilibrium is excluded in the nonrandom $l_1$ case, it is proved to occur for both short and long range potentials for Gaussian distributions, and for potentials of class $l_2$ in the Bernoulli case. Open problems are discussed.Comment: 10 pages, no figures. This last version, to appear in J. Stat. Phys., corrects some minor errors and includes additional references and comments on the relation to experiment