The Evaluation of the Collision Matrix

Wick, G. C.

doi:10.1103/physrev.80.268

Cited by 1,095 publications

(696 citation statements)

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“…Since, once again, the proof is the same as in [9], we check this statement for the purpose of illustration in the case of the mixed product note that the (ill defined) general contraction : φ(y)φ(y 1 )φ(y 2 ) : is missing.…”

Section: A the Second General Wick Theoremmentioning

confidence: 97%

“…The argument is exactly the same as in the original proof of Wick [9], which only relies on the fact that [φ(x), [φ + (x ), φ − (x )]] = 0; the particular choice of a rule by which the times τ, τ , τ are associated to x, x , x plays no role. Here, we will content ourselves with checking the first Wick theorem in the simplest case: consider…”

Section: Jhep08(2004)031mentioning

confidence: 99%

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Non Local Theories: New Rules for Old Diagrams

Piacitelli¹

2004

J. High Energy Phys.

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Abstract:We show that a general variant of the Wick theorems can be used to reduce the time ordered products in the Gell-Mann & Low formula for a certain class on non local quantum field theories, including the case where the interaction lagrangian is defined in terms of twisted products. The only necessary modification is the replacement of the Stueckelberg-Feynman propagator by the general propagator (the "contractor" of Denk and Schweda)where the violations of locality and causality are represented by the dependence of τ, τ on other points, besides those involved in the contraction. This leads naturally to a diagrammatic expansion of the Gell-Mann & Low formula, in terms of the same diagrams as in the local case, the only necessary modification concerning the Feynman rules. The ordinary local theory is easily recovered as a special case, and there is a one-to-one correspondence between the local and non local contributions corresponding to the same diagrams, which is preserved while performing the large scale limit of the theory.

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Section: A the Second General Wick Theoremmentioning

confidence: 97%

Section: Jhep08(2004)031mentioning

confidence: 99%

Non Local Theories: New Rules for Old Diagrams

Piacitelli¹

2004

J. High Energy Phys.

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“…con is zero for all N > 2, the higher-order correlation functions factorise and are given by the Wick decomposition [14,15] containing only terms of G (N ) with N ≤ 2. In this case, the quantum many-body states are Gaussian.…”

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confidence: 99%

Experimental characterization of a quantum many-body system via higher-order correlations

Schweigler

Kasper

Erne

et al. 2017

Nature

243

319

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“…dependence is a consequence of Wick's theorem 3 , which enables higher-order correlations to be expressed using products of one-body correlation functions. The applicability of Wick's theorem is not limited to just correlation functions for light, it has been also applied in many other fields; for example, it is commonly used in radioastronomy, nuclear physics 7 , and generally in quantum field theory 3 . The validity of Wick's theorem has been demonstrated with thermal photons, however, so far there have been no direct measurements demonstrating its validity to higher orders for massive particles.…”

mentioning

confidence: 99%

“…To provide further detail on the three-body correlation function g (3) ( z) in Fig. 2b, we have also plotted in Fig.…”

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confidence: 99%

Ideal n-body correlations with massive particles

et al. 2013

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In 1963 Glauber introduced the modern theory of quantum coherence 1 , which extended the concept of first-order (onebody) correlations, describing phase coherence of classical waves, to include higher-order (n-body) quantum correlations characterizing the interference of multiple particles. Whereas the quantum coherence of photons is a mature cornerstone of quantum optics, the quantum coherence properties of massive particles remain largely unexplored. To investigate these properties, here we use a uniquely correlated 2 source of atoms that allows us to observe n-body correlations up to the sixthorder at the ideal theoretical limit (n!). Our measurements constitute a direct demonstration of the validity of one of the most widely used theorems in quantum many-body theory-Wick's theorem 3 -for a thermal ensemble of massive particles. Measurements involving n-body correlations may play an important role in the understanding of thermalization of isolated quantum systems 4 and the thermodynamics of exotic many-body systems, such as Efimov trimers 5 .Glauber's modern theory of optical coherence and the famous Hanbury Brown-Twiss effect 6 were pivotal in the establishment of the field of quantum optics. Importantly, the definition of a coherent state required coherence to all orders, which for example distinguishes a monochromatic but incoherent thermal source of light from a truly coherent source such as a laser. Higher-order correlation functions therefore provide a more rigorous test of coherence.Higher-order correlations, characterized by an n-body correlation function g (n) , are of general interest and have been investigated in many fields of physics including astronomy 6 , particle physics 7 , quantum optics 8 , and quantum atom optics 9 . In particular they have been a fruitful area of research in the field of quantum optics, where they have been used to investigate the properties of laser light, including heralded single photons 10 , and the statistics of parametric down-conversion sources 11 . State-of-the-art quantum optics experiments have measured photon correlation functions up to sixth order for quasi-thermal sources 8 , allowing the possibility of performing full quantum state tomography 12 .Higher-order correlations experiments with massive particles are currently approaching the same level of maturity as with photons. So far, experiments have directly observed correlations up to fourth order with single-atom-sensitive detection techniques for ultracold atomic bosons 9,13,14 , and second-order correlations for an atomic source of fermions 15 demonstrating the uniquely quantum mechanical property of atom-atom antibunching. Alternative, indirect techniques have also been employed to investigate higher-order correlations, including the measurements of twobody (photoassociation 16 ) and three-body 17 loss rates that are sensitive, respectively, to second-and third-order correlation functions. Interestingly, fermionic atom pairs 18 and fermionic antibunching 19 have also been observed in the atomic shot no...

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The Evaluation of the Collision Matrix

Cited by 1,095 publications

References 4 publications

Non Local Theories: New Rules for Old Diagrams

Non Local Theories: New Rules for Old Diagrams

Experimental characterization of a quantum many-body system via higher-order correlations

Ideal n-body correlations with massive particles

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