Free-field operators: Time evolution and commutation relations

2016 ◽  
pp. 227-234
1957 ◽  
Vol 53 (4) ◽  
pp. 843-847 ◽  
Author(s):  
J. C. Polkinghorne

ABSTRACTThe Yang-Feldman formalism vising the Feynman-like Green's functions is set up. The corresponding free fields have non-trivial commutation relations and contain information about the scattering. S-matrix elements are simply the matrix elements of anti-normal products of the field φF′(x). These are evaluated, and they give directly expressions used in the theory of causality and dispersion relations. It is possible to formulate field theory in a form in which the fields obey free field equations and the effects of interaction are contained in their commutation relations.


Author(s):  
K. R. Parthasarathy

It is well-known3,5 that Brownian motion and Poisson process arise naturally from the canonical commutation relations (CCR) of free field operators in a boson Fock space. Eyre and Hudson2 have recently shown how to construct fields of operators in a boson Fock space obeying super Lie commutation relations. We establish the essential self-adjointness of their real and imaginary parts on the domain ∊, the linear manifold generated by all the exponential (coherent) vectors and determine a family of Markov processes which they give rise to in a natural manner. These Markov processes yield examples of Evans–Hudson flows3,5 and Azéma-like martingales.1,4,6


2011 ◽  
Vol 26 (02) ◽  
pp. 127-138 ◽  
Author(s):  
V. ALDAYA ◽  
M. CALIXTO ◽  
F. F. LÓPEZ-RUIZ

We explore the O(N)-invariant Non-Linear Sigma Model (NLSM) in a different perturbative regime from the usual relativistic-free-field one, by using non-canonical basic commutation relations adapted to the underlying O(N) symmetry of the system, which also account for the nontrivial (nonflat) geometry and topology of the target manifold.


2019 ◽  
Vol 62 (3) ◽  
pp. 745-757 ◽  
Author(s):  
Jessica M. Wess ◽  
Joshua G. W. Bernstein

PurposeFor listeners with single-sided deafness, a cochlear implant (CI) can improve speech understanding by giving the listener access to the ear with the better target-to-masker ratio (TMR; head shadow) or by providing interaural difference cues to facilitate the perceptual separation of concurrent talkers (squelch). CI simulations presented to listeners with normal hearing examined how these benefits could be affected by interaural differences in loudness growth in a speech-on-speech masking task.MethodExperiment 1 examined a target–masker spatial configuration where the vocoded ear had a poorer TMR than the nonvocoded ear. Experiment 2 examined the reverse configuration. Generic head-related transfer functions simulated free-field listening. Compression or expansion was applied independently to each vocoder channel (power-law exponents: 0.25, 0.5, 1, 1.5, or 2).ResultsCompression reduced the benefit provided by the vocoder ear in both experiments. There was some evidence that expansion increased squelch in Experiment 1 but reduced the benefit in Experiment 2 where the vocoder ear provided a combination of head-shadow and squelch benefits.ConclusionsThe effects of compression and expansion are interpreted in terms of envelope distortion and changes in the vocoded-ear TMR (for head shadow) or changes in perceived target–masker spatial separation (for squelch). The compression parameter is a candidate for clinical optimization to improve single-sided deafness CI outcomes.


1988 ◽  
Vol 31 (2) ◽  
pp. 156-165 ◽  
Author(s):  
P. A. Busby ◽  
Y. C. Tong ◽  
G. M. Clark

The identification of consonants in a/-C-/a/nonsense syllables, using a fourteen-alternative forced-choice procedure, was examined in 4 profoundly hearing-impaired children under five conditions: audition alone using hearing aids in free-field (A),vision alone (V), auditory-visual using hearing aids in free-field (AV1), auditory-visual with linear amplification (AV2), and auditory-visual with syllabic compression (AV3). In the AV2 and AV3 conditions, acoustic signals were binaurally presented by magnetic or acoustic coupling to the subjects' hearing aids. The syllabic compressor had a compression ratio of 10:1, and attack and release times were 1.2 ms and 60 ms. The confusion matrices were subjected to two analysis methods: hierarchical clustering and information transmission analysis using articulatory features. The same general conclusions were drawn on the basis of results obtained from either analysis method. The results indicated better performance in the V condition than in the A condition. In the three AV conditions, the subjects predominately combined the acoustic parameter of voicing with the visual signal. No consistent differences were recorded across the three AV conditions. Syllabic compression did not, therefore, appear to have a significant influence on AV perception for these children. A high degree of subject variability was recorded for the A and three AV conditions, but not for the V condition.


2002 ◽  
Vol 16 (2) ◽  
pp. 114-118 ◽  
Author(s):  
Timo Ruusuvirta ◽  
Heikki Hämäläinen

Abstract Human event-related potentials (ERPs) to a tone continuously alternating between its two spatial loci of origin (middle-standards, left-standards), to repetitions of left-standards (oddball-deviants), and to the tones originally representing these repetitions presented alone (alone-deviants) were recorded in free-field conditions. During the recordings (Fz, Cz, Pz, M1, and M2 referenced to nose), the subjects watched a silent movie. Oddball-deviants elicited a spatially diffuse two-peaked deflection of positive polarity. It differed from a deflection elicited by left-standards and commenced earlier than a prominent deflection of negative polarity (N1) elicited by alone-deviants. The results are discussed in the context of the mismatch negativity (MMN) and previous findings of dissociation between spatial and non-spatial information in auditory working memory.


1999 ◽  
Author(s):  
W. Todd Nelson ◽  
Robert S. Bolia ◽  
Mark A. Ericson ◽  
Richard L. McKinley

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