16 results on '"Liegener, Klaus"'
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2. Modifications to gravitational wave equation from canonical quantum gravity
- Author
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Dapor, Andrea and Liegener, Klaus
- Published
- 2020
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3. Expectation values of coherent states for SU(2) Lattice Gauge Theories
- Author
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Liegener, Klaus and Zwicknagel, Ernst-Albrecht
- Published
- 2020
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4. Properties of the Hamiltonian Renormalisation and its application to quantum mechanics on the circle
- Author
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Bahr, Benjamin and Liegener, Klaus
- Subjects
High Energy Physics - Lattice ,High Energy Physics - Lattice (hep-lat) ,FOS: Physical sciences ,General Relativity and Quantum Cosmology (gr-qc) ,Mathematical Physics (math-ph) ,General Relativity and Quantum Cosmology ,Mathematical Physics - Abstract
We consider the Hamiltonian renormalisation group flow of discretised one-dimensional physical theories. In particular, we investigate the influence the choice of different embedding maps has on the RG flow and the resulting continuum limit, and show in which sense they are, and in which sense they are not equivalent as physical theories. We are furthermore elucidating the interplay of the RG flow and the algebras operators satisfy, both on the discrete and the continuum. Further, we propose preferred renormalisation prescriptions for operator algebras guaranteeing to arrive at preferred algebraic relations in the continuum, if suitable extension properties are assumed. Finally, we introduce a weaker form of distributional equivalence, and show how unitarily inequivalent continuum limits, which arise due to a choice of different embedding maps, can still be weakly equivalent in that sense., 16 pages
- Published
- 2021
5. Algorithmic approach to Cosmological Coherent State Expectation Values in LQG
- Author
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Liegener, Klaus and Rudnicki, Łukasz
- Subjects
High Energy Physics - Lattice ,General Relativity and Quantum Cosmology - Abstract
In the lattice approach to Loop Quantum Gravity on a fixed graph computations tend to be involved and are rarely analytically manageable. But, when interested in the expectation values of coherent states on the lattice which are sharply peaked on isotropic, flat cosmology several simplifications are possible which reduce the computational effort. We present a step-by-step algorithm resulting in an analytical expression including up to first order corrections in the spread of the state. The algorithm is developed in such a way that it makes the computation straightforward and easy to be implementable in programming languages such as Mathematica. Exemplarily, we demonstrate how the algorithm streamlines the road to obtain the expectation value of the euclidean part of the scalar constraint and as a consistency check perform the analytic computation as well. To showcase further applications of the algorithm, we investigate the fate of the effective dynamics program custom in Loop Cosmology and find that the next-to-leading order corrections can {\it not} be used as corrections for an effective Hamiltonian., Comment: 33 pages; This paper summarizes the results announced at Loops'19 Conference [http://gravity.psu.edu/events/loops19/index-loops19.shtml]. First draft - minor typos can still be found
- Published
- 2020
6. Renormierung in der Schleifenquantengravitation
- Author
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Liegener, Klaus
- Subjects
ddc:539 ,Naturwissenschaftliche Fakultät - Abstract
In this thesis, we will investigate the quantisation ambiguities that arise during the canonical quantisation of General Relativity (GR), and we will develop a method of Hamiltonian renormalisation to fix the mentioned ambiguities. ''Quantisation'' is an ansatz to obtain a fundamental (i.e. quantum) theory from a classical description. However, there is no way to ''derive'' this more complex framework if we only know a special case of it, i.e. its classical pendant. Hence, quantisation contains a lot of possible choices and must be supplemented by mathematical consistency and experimental evidence. In the case of gravity, whose effects are described by GR, no experiments are known which reveal properties of its quantum nature. Thus, we must rely purely on mathematical rigour to obtain a version of Quantum Gravity (QG). A promising candidate for this endeavour is ''Loop Quantum Gravity'' (LQG), a modern version of the canonical or Hamiltonian approach. During its development over the past 30 years, it achieved to describe a well-defined canonical quantum field theory. LQG presented a unique Hilbert space representation and the quantisation of constraints as operators acting thereon. During quantisation one must make certain choices by introducing ''regularisation parameters''. However, the details of the operators will be influenced by these choices even in the limit of vanishing regularisation parameters. Their varying physical predictions present an unsatisfactory situation as it is not clear which of those describe the real world. The present work adapts the techniques from the covariant ''renormalisation group'' from Quantum Field Theory (QFT) to LQG. The philosophy of this machinery is that continuum theories should provide a consistent description, no matter with what resolution one looks at the system under consideration. This tool has been used in the context of defining other quantum field theories via the path integral framework. It turned out to be very successful and is, as of today, one of the main tools for studying weak and strong interaction in the Standard Model of particle physics. But, since the mathematical language of canonical QG is vastly different, we will translate the renormalisation group from covariant QFT. Afterwards, we will test it on a simple model, i.e. the massive free scalar field in arbitrary dimensions, and we will present a detailed analysis of it. This includes robustness of the fixed point under different choices of the renormalisation map and the fixed point's range of attraction. Also, we study properties of the discrete projections such as the perfect lattice Laplacian and restoration of continuum symmetries. Finally, we will show the non-trivial impact of quantisation ambiguities in the context of LQG, which can already be seen in cosmological models describing our universe at large scales. Despite these drawbacks, the recent developments in the field allowed to pinpoint the caveats due to their mathematically precise formulation and suggest renormalisation techniques as a possible future improvement. It turns out that the new framework of direct Hamiltonian renormalisation serves as a good candidate to resolve the quantisation ambiguities plaguing QG.
- Published
- 2019
7. Cosmological effective Hamiltonian from full loop quantum gravity dynamics
- Author
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Dapor, Andrea and Liegener, Klaus
- Published
- 2018
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8. Symmetry restriction and its application to gravity.
- Author
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Kamiński, Wojciech and Liegener, Klaus
- Subjects
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GENERAL relativity (Physics) , *SYMMETRIC spaces , *SYMMETRY , *PHASE space , *GRAVITY , *QUANTUM gravity - Abstract
In the Hamiltonian formulation, it is not a priori clear whether a symmetric configuration will keep its symmetry during evolution. In this paper, we give precise requirements of when this is the case and propose a symmetry restriction to the phase space of the symmetric variables. This can often ease computation, especially when transcending from the infinite dimensional phase space of a field theory to a possibly finite dimensional subspace. We will demonstrate this in the case of gravity. A prominent example is the restriction of full general relativity in its Hamiltonian formulation to the cosmological configurations of Robertson–Walker type. We will demonstrate our procedure in this setting and extend it to examples that appear useful in certain approaches to quantum gravity. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
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9. Matrix Elements of Lorentzian Hamiltonian Constraint in LQG
- Author
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Alesci, Emanuele, Liegener, Klaus, and Zipfel, Antonia
- Subjects
General Relativity and Quantum Cosmology ,FOS: Physical sciences ,General Relativity and Quantum Cosmology (gr-qc) - Abstract
The Hamiltonian constraint is the key element of the canonical formulation of LQG coding its dynamics. In Ashtekar-Barbero variables it naturally splits into the so called Euclidean and Lorentzian parts. However, due to the high complexity of this operator, only the matrix elements of the Euclidean part have been considered so far. Here we evaluate the action of the full constraint, including the Lorentzian part. The computation requires an heavy use of SU(2) recoupling theory and several tricky identities among n-j symbols are used to find the final result: these identities, together with the graphical calculus used to derive them, also simplify the Euclidean constraint and are of general interest in LQG computations., 36 pages, minor typos corrected
- Published
- 2013
10. Matrix elements of Lorentzian Hamiltonian constraint in loop quantum gravity.
- Author
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Alesci, Emanuele, Liegener, Klaus, and Zipfel, Antonia
- Subjects
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LORENTZIAN function , *HAMILTON'S equations , *LOOP quantization , *EUCLIDEAN geometry , *SPIN-spin interactions - Abstract
The Hamiltonian constraint is the key element of the canonical formulation of loop quantum gravity (LQG) coding its dynamics. In Ashtekar-Barbero variables it naturally splits into the so-called Euclidean and Lorentzian parts. However, due to the high complexity of this operator, only the matrix elements of the Euclidean part have been considered so far. Here we evaluate the action of the full constraint, including the Lorentzian part. The computation requires heavy use of SU(2) recoupling theory and several tricky identities among n-j symbols are used to find the final result: these identities, together with the graphical calculus used to derive them, also simplify the Euclidean constraint and are of general interest in LQG computations. [ABSTRACT FROM AUTHOR]
- Published
- 2013
- Full Text
- View/download PDF
11. Effective LQC model for k=+1 isotropic cosmologies from spatial discretizations.
- Author
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Liegener, Klaus and Weigl, Stefan Andreas
- Subjects
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PHASE space , *PHYSICAL cosmology , *MOTIVATION (Psychology) - Abstract
The closed, spatially isotropic Friedmann-Lemaître-Robertson-Walker universe (k=+1) is endowed with modifications due to a discrete underlying space-structure. Motivated from loop quantum gravity techniques, a full Thiemann regularization is performed. The impact of these modifications of the single-graph-sector appearing in the scalar constraint are interpreted as physical quantum gravity effects. We investigate the form of the modified scalar constraint and its analytical approximations for k=+1 spacetimes and assume this effective constraint as the generator of dynamics on the reduced isotropic phase space. It transpires that the system still features a classical recollapse with only marginal discreteness corrections. Moreover, the initial and final singularities are resolved and we present an effective model mirroring the qualitative features of system. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
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12. Some physical implications of regularization ambiguities in SU(2) gauge-invariant loop quantum cosmology.
- Author
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Liegener, Klaus and Singh, Parampreet
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QUANTUM cosmology , *COSMOLOGICAL constant , *MATHEMATICAL regularization , *QUANTUM gravity , *AMBIGUITY , *REGULARIZATION parameter - Abstract
The way physics of loop quantum gravity is affected by the underlying quantization ambiguities is an open question. We address this issue in the context of loop quantum cosmology using gauge-covariant fluxes. Consequences are explored for two choices of regularization parameters: μ0 and μ̄ in the presence of a positive cosmological constant, and two choices of regularizations of the Hamiltonian constraint in loop quantum cosmology: the standard and the Thiemann regularization. We show that novel features of singularity resolution and bounce, occurring due to gauge-covariant fluxes, exist also for Thiemann-regularized dynamics. The μ0 scheme is found to be unviable as in standard loop quantum cosmology when a positive cosmological constant is included. Our investigation brings out a surprising result that the nature of emergent matter in the prebounce regime is determined by the choice of regulator in the Thiemann regularization of the scalar constraint whether or not one uses gauge-covaraint fluxes. Unlike the μ̄ scheme where the emergent matter is a cosmological constant, the emergent matter in the μ0 scheme behaves as a string gas. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
13. New loop quantum cosmology modifications from gauge-covariant fluxes.
- Author
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Liegener, Klaus and Singh, Parampreet
- Subjects
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QUANTUM cosmology , *QUANTUM gravity , *COHERENT states , *GAUGE field theory , *PLANCK scale , *QUANTUM theory , *REGULARIZATION parameter - Abstract
Loop quantum cosmology is a symmetry reduced quantization of cosmological spacetimes based on loop quantum gravity. While it has been successful in resolution of various cosmological singularities and connecting Planck scale physics to phenomenology, its connection with loop quantum gravity has remained elusive. It is therefore important to integrate more and more features of the full theory into this framework and understand the reliability of physical predictions. In particular, if one wishes to connect the effective Hamiltonian in loop quantum cosmology to an expectation value of the scalar constraint operator in suitable coherent states for the full theory, one has to go beyond the standard setting of loop quantum cosmology. One possibility is to introduce gauge-covariant fluxes, which become necessary because the presence of a finite regularization parameter causes functions built out of the standard discretized variables to be in general not gauge invariant. Following the construction of gauge-covariant fluxes pioneered by Thiemann [Quantum spin dynamics (QSD): VII. Symplectic structures and continuum lattice formulations of gauge field theories, Classical Quantum Gravity 18, 3293 (2001)], we show that the physics of loop quantum cosmology is affected in a nontrivial way. The bounce turns out to be generically asymmetric with a rescaling of Newton's constant in the prebounce branch. Gauge-covariant fluxes result in a higher order quantum difference equation in comparison to loop quantum cosmology. Even the behavior of matter, which behaves innocuously in loop quantum cosmology, is enriched resulting in an effective nonminimal coupling. These effects are shown to be common to different choices of regularization parameters. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
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14. Challenges in recovering a consistent cosmology from the effective dynamics of loop quantum gravity.
- Author
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Dapor, Andrea, Liegener, Klaus, and Pawłowski, Tomasz
- Subjects
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QUANTUM theory , *PHYSICAL cosmology , *HAMILTONIAN graph theory , *QUANTUM gravity - Abstract
We reexamine a set of existing procedures aimed at recovering the effective description of the dynamics of loop quantum gravity in the context of cosmological solutions. In particular, the studies of those methods, to which the choice of cuboidal graphs and graph-preserving Hamiltonian is central, result in the formulation of a set of no-go statements, severely limiting the possibility of recovering a physically consistent effective dynamics this way. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
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15. Perspectives on the dynamics in a loop quantum gravity effective description of black hole interiors.
- Author
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Assanioussi, Mehdi, Dapor, Andrea, and Liegener, Klaus
- Subjects
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QUANTUM theory , *BLACK holes , *QUANTUM gravity , *QUANTUM operators , *PHASE space , *HAMILTONIAN operator , *SPACETIME - Abstract
In the loop quantum gravity context, there have been numerous proposals to quantize the reduced phase space of a black hole and develop a classical effective description for its interior which eventually resolves the singularity. However, little progress has been made toward understanding the relation between such quantum/effective minisuperspace models and what would be the spherically symmetric sector of loop quantum gravity. In particular, it is not clear whether one can extract the phenomenological predictions obtained in minisuperspace models, such as the singularity resolution and the spacetime continuation beyond the singularity, based on results in full loop quantum gravity. In this paper, we present an attempt in this direction in the context of Kantowski-Sachs spacetime, through the proposal of two new effective Hamiltonians for the reduced classical model. The first is derived using Thiemann classical identities for the regularized expressions, while the second is obtained as a first approximation of the expectation value of a Hamiltonian operator in loop quantum gravity in a semiclassical state peaked on the Kantowski-Sachs initial data. We then proceed with a detailed analysis of the dynamics they generate and compare them with the Hamiltonian derived in general relativity and the common effective Hamiltonian proposed in earlier literature. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
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16. Emergent de Sitter Epoch of the Quantum Cosmos from Loop Quantum Cosmology.
- Author
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Assanioussi, Mehdi, Dapor, Andrea, Liegener, Klaus, and Pawłowski, Tomasz
- Subjects
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QUANTUM cosmology , *COSMOLOGICAL constant ,UNIVERSE - Abstract
The quantum nature of the big bang is reexamined in the framework of loop quantum cosmology. The strict application of a regularization procedure to the Hamiltonian, originally developed for the Hamiltonian in loop quantum gravity, leads to a qualitative modification of the bounce paradigm. Quantum gravity effects still lead to a quantum bounce connecting deterministically large classical universes. However, the evolution features a large epoch of a de Sitter universe, with an emergent cosmological constant of Planckian order, smoothly transiting into a spatially flat expanding universe. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
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