is there a study/research/citation maxxing guide?

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want to learn how to research and cite papers to sound more high iq

 

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Plastic and Reconstructive Surgery

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[Deleted member 15854]

Plastic and Reconstructive Surgery

journals.lww.com

Google Scholar

Met Google Scholar kun je gemakkelijk brede zoekopdrachten naar wetenschappelijke literatuur uitvoeren. Doorzoek veel verschillende vakgebieden en bronnen: artikelen, scripties, boeken, samenvattingen en uitspraken van rechtbanken.

scholar.google.com

Sci-Hub: knowledge belongs to all mankind

Sci-Hub website. Get free access to academic journals. Download research papers for free from ScienceDirect, IEEE, Wiley, Springer, Nature and others

scihub.unblockit.ist

Dermatology Times and Multimedia Medical, LLC

www.dermatologytimes.com

omg tanks u babes! i am 200 iq now


String theory is one of the most promising candidates for bridging the gap between QFT and general relativity theory by supplying a unified theory of all natural forces, including gravitation. The basic idea of string theory is not to take particles as fundamental objects but strings that are very small but extended in one dimension. This assumption has the pivotal consequence that strings interact on an extended distance and not at a point. This difference between string theory and standard QFT is essential because it is the reason why string theory also encompasses the gravitational force which is very difficult to deal with in the framework of QFT.

It is so hard to reconcile gravitation with QFT because the typical length scale of the gravitational force is very small, namely at Planck scale, so that the quantum field theoretical assumption of point-like interaction leads to untreatable infinities. To put it another way, gravitation becomes significant (in particular in comparison to strong interaction) exactly where QFT is most severely endangered by infinite quantities. The extended interaction of strings brings it about that such infinities can be avoided. In contrast to the entities in standard quantum physics strings are not characterized by quantum numbers but only by their geometrical and dynamical properties. Nevertheless, “macroscopically” strings look like quantum particles with quantum numbers. A basic geometrical distinction is the one between open strings, i.e., strings with two ends, and closed strings which are like bracelets. The central dynamical property of strings is their mode of excitation, i.e., how they vibrate.

Reservations about string theory are mostly due to the lack of testability since it seems that there are no empirical consequences which could be tested by the methods which are, at least up to now, available to us. The reason for this “problem” is that the length scale of strings is in the average the same as the one of quantum gravity, namely the Planck length of approximately 10−33

centimeters which lies far beyond the accessibility of feasible particle experiments. But there are also other peculiar features of string theory which might be hard to swallow. One of them is the fact that preferred models of string theory need space-time with 10, 11 or even 26 dimensions. In order to explain the appearance of only four space-time dimensions string theory assumes that the other dimensions are somehow folded away or “compactified” so that they are no longer visible. An intuitive idea can be gained by thinking of a macaroni which is a tube, i.e., a two-dimensional piece of pasta rolled together, but which looks from the distance like a one-dimensional string.

Due to the problems of string theory, many physicists have abandoned it, but not all. Some think that, among the numerous alternative proposals for reconciling quantum physics and general relativity theory, string theory is still the best candidate, with “loop quantum gravity” as its strongest rival (see the entry on quantum gravity). Correspondingly, string theory has also received some attention within the philosophy of physics community in recent years. Probably the first philosophical investigation of string theory is Weingard (2001) in Callender & Huggett (2001), an anthology with further related articles. Dawid (2003) (see Other Internet Resources below) argues that string theory has significant consequences for the philosophical debate about realism, namely that it speaks against the plausibility of anti-realistic positions. Also see Dawid (2009). Johansson and Matsubara (2011) assess string theory from various different methodological perspectives, reaching conclusions in disagreement with Dawid (2009). Standard introductory monographs on string theory are Polchinski (2000) and Kaku (1999). Greene (1999) is a very successful popular introduction. An interactive website with a nice elementary introduction is ‘Stringtheory.com’ (see the Other Internet Resources section below).

4. Axiomatic Reformulations of QFT and their Interpretive Significance​

There are three main motives for reformulating conventional QFT. The first motive is operationalism, the second one mathematical rigour and the third one finding a way to deal with the availability of inequivalent Hilbert space representations for systems with an infinite number of degrees of freedom, such as fields. While in principle the three motives are independent of one another there are multiple interconnections in their actual implementation. One way in which the three motives are connected is the following: In QFT the quests for operationalism and mathematical rigour seem to go hand in hand, i.e. the best means to achieve one is also the best way to achieve the other. Moreover, it leads to an algebraic formulation that avoids privileging one amoung various available inequivalent representations, which tacitly happens in conventional QFT.

4.1 Motive One: Operationalism​

The first motive–operationalism–is not so higly valued any more today, and for good reasons (see entry on Operationalism). Nevertheless, it was, not only in physics, very strong in and around the 1950s, when axiomatic reformulations of QFT entered the scene. Accordingly, the impact of operationalism must not by overlooked. Already in the 1930s the problem of perturbative infinities (see Supplement “The History of QFT”) as well as the potentially heuristic status of the Lagrangian formulation of QFT stimulated the search for concise and ideally axiomatic reformulations. About a dacade later it became clear that operationalism and mathematical rigour may go hand in hand, because the setting of conventional QFT—where quantum fields are basic, with field values being assigned to points in spacetime—is both mathematically ill-defined and in conflict with the “operational” idea that the core elements of an empirical theory should be observable quantities, which can be measured by means of certain physical operations.

The mathematical aspect of the problem is that a field at a point, ϕ(x)

, is not an operator on a Hilbert space. The physical counterpart of the problem is that it would require an infinite amount of energy to measure a field at a point of space-time. One way to handle this situation—and one of the starting points for axiomatic reformulations of QFT—is not to consider fields at a point but instead fields which are smeared out in the vicinity of that point using certain functions, so-called test functions. The result is a smeared field ϕ(f)=∫ϕ(x)f(x)dx with supp(f)⊂O, where supp(f) is the support of the test function f and O is a bounded open region in Minkowski space-time. In Wightman’s field axiomatics from the early 1950s, the basic entities are then polynomial algebras P(O) of smeared fields, i.e., sums of products of smeared fields in finite space-time regions O. Thus it replaces the mapping x→ϕ(x) in the conventional formulation of QFT by O→P(O)
.

From an operationalist perspective equally troublesome as point-like quantities are global quantities, like total charge, total energy or total momentum of a field. They are unobservable since their measurement would have to take place in the whole universe. Accordingly, quantities which refer to infinitely extended regions of space-time should not appear among the observables of the theory, as they do in the standard formulation of QFT. In the discussion of such “parochial observables” below we will see that it is not so clear in the end whether this is really a good argument (see Ruetsche 2011 and Feintzeig 2018). In any case, however, it has been important in the formation of axiomatic reformulations of QFT.

Another operationalist reason for favouring algebraic formulations derives from the fact that two quantum fields are physically equivalent when they generate the same algebras of local observables. Such equivalent quantum field theories belong to the same so-called Borchers class which entails that they lead to the same S

-matrix. As Haag (1996) stresses, fields are only an instrument in order to “coordinatize” observables, more precisely: sets of observables, with respect to different finite space-time regions. The choice of a particular field system is to a certain degree conventional, namely as long as it belongs to the same Borchers class. Thus it is more appropriate to consider these algebras, rather than quantum fields, as the fundamental entities in QFT. The resulting operationalistic view of QFT is that it is a statistical theory about local measurement outcomes, expressed in terms of local algebras of observables. Thus, it is no surprise that Haag’s (1996) famous textbook on “Algebraic QFT”, the most successful axiomatic reformulation, bears the title “Local Quantum Physics.”

​

 

[deepweb1298]

omg tanks u babes! i am 200 iq now


String theory is one of the most promising candidates for bridging the gap between QFT and general relativity theory by supplying a unified theory of all natural forces, including gravitation. The basic idea of string theory is not to take particles as fundamental objects but strings that are very small but extended in one dimension. This assumption has the pivotal consequence that strings interact on an extended distance and not at a point. This difference between string theory and standard QFT is essential because it is the reason why string theory also encompasses the gravitational force which is very difficult to deal with in the framework of QFT.

It is so hard to reconcile gravitation with QFT because the typical length scale of the gravitational force is very small, namely at Planck scale, so that the quantum field theoretical assumption of point-like interaction leads to untreatable infinities. To put it another way, gravitation becomes significant (in particular in comparison to strong interaction) exactly where QFT is most severely endangered by infinite quantities. The extended interaction of strings brings it about that such infinities can be avoided. In contrast to the entities in standard quantum physics strings are not characterized by quantum numbers but only by their geometrical and dynamical properties. Nevertheless, “macroscopically” strings look like quantum particles with quantum numbers. A basic geometrical distinction is the one between open strings, i.e., strings with two ends, and closed strings which are like bracelets. The central dynamical property of strings is their mode of excitation, i.e., how they vibrate.

Reservations about string theory are mostly due to the lack of testability since it seems that there are no empirical consequences which could be tested by the methods which are, at least up to now, available to us. The reason for this “problem” is that the length scale of strings is in the average the same as the one of quantum gravity, namely the Planck length of approximately 10−33

centimeters which lies far beyond the accessibility of feasible particle experiments. But there are also other peculiar features of string theory which might be hard to swallow. One of them is the fact that preferred models of string theory need space-time with 10, 11 or even 26 dimensions. In order to explain the appearance of only four space-time dimensions string theory assumes that the other dimensions are somehow folded away or “compactified” so that they are no longer visible. An intuitive idea can be gained by thinking of a macaroni which is a tube, i.e., a two-dimensional piece of pasta rolled together, but which looks from the distance like a one-dimensional string.

Due to the problems of string theory, many physicists have abandoned it, but not all. Some think that, among the numerous alternative proposals for reconciling quantum physics and general relativity theory, string theory is still the best candidate, with “loop quantum gravity” as its strongest rival (see the entry on quantum gravity). Correspondingly, string theory has also received some attention within the philosophy of physics community in recent years. Probably the first philosophical investigation of string theory is Weingard (2001) in Callender & Huggett (2001), an anthology with further related articles. Dawid (2003) (see Other Internet Resources below) argues that string theory has significant consequences for the philosophical debate about realism, namely that it speaks against the plausibility of anti-realistic positions. Also see Dawid (2009). Johansson and Matsubara (2011) assess string theory from various different methodological perspectives, reaching conclusions in disagreement with Dawid (2009). Standard introductory monographs on string theory are Polchinski (2000) and Kaku (1999). Greene (1999) is a very successful popular introduction. An interactive website with a nice elementary introduction is ‘Stringtheory.com’ (see the Other Internet Resources section below).

4. Axiomatic Reformulations of QFT and their Interpretive Significance​

There are three main motives for reformulating conventional QFT. The first motive is operationalism, the second one mathematical rigour and the third one finding a way to deal with the availability of inequivalent Hilbert space representations for systems with an infinite number of degrees of freedom, such as fields. While in principle the three motives are independent of one another there are multiple interconnections in their actual implementation. One way in which the three motives are connected is the following: In QFT the quests for operationalism and mathematical rigour seem to go hand in hand, i.e. the best means to achieve one is also the best way to achieve the other. Moreover, it leads to an algebraic formulation that avoids privileging one amoung various available inequivalent representations, which tacitly happens in conventional QFT.

4.1 Motive One: Operationalism​

The first motive–operationalism–is not so higly valued any more today, and for good reasons (see entry on Operationalism). Nevertheless, it was, not only in physics, very strong in and around the 1950s, when axiomatic reformulations of QFT entered the scene. Accordingly, the impact of operationalism must not by overlooked. Already in the 1930s the problem of perturbative infinities (see Supplement “The History of QFT”) as well as the potentially heuristic status of the Lagrangian formulation of QFT stimulated the search for concise and ideally axiomatic reformulations. About a dacade later it became clear that operationalism and mathematical rigour may go hand in hand, because the setting of conventional QFT—where quantum fields are basic, with field values being assigned to points in spacetime—is both mathematically ill-defined and in conflict with the “operational” idea that the core elements of an empirical theory should be observable quantities, which can be measured by means of certain physical operations.

The mathematical aspect of the problem is that a field at a point, ϕ(x)

, is not an operator on a Hilbert space. The physical counterpart of the problem is that it would require an infinite amount of energy to measure a field at a point of space-time. One way to handle this situation—and one of the starting points for axiomatic reformulations of QFT—is not to consider fields at a point but instead fields which are smeared out in the vicinity of that point using certain functions, so-called test functions. The result is a smeared field ϕ(f)=∫ϕ(x)f(x)dx with supp(f)⊂O, where supp(f) is the support of the test function f and O is a bounded open region in Minkowski space-time. In Wightman’s field axiomatics from the early 1950s, the basic entities are then polynomial algebras P(O) of smeared fields, i.e., sums of products of smeared fields in finite space-time regions O. Thus it replaces the mapping x→ϕ(x) in the conventional formulation of QFT by O→P(O)
.

From an operationalist perspective equally troublesome as point-like quantities are global quantities, like total charge, total energy or total momentum of a field. They are unobservable since their measurement would have to take place in the whole universe. Accordingly, quantities which refer to infinitely extended regions of space-time should not appear among the observables of the theory, as they do in the standard formulation of QFT. In the discussion of such “parochial observables” below we will see that it is not so clear in the end whether this is really a good argument (see Ruetsche 2011 and Feintzeig 2018). In any case, however, it has been important in the formation of axiomatic reformulations of QFT.

Another operationalist reason for favouring algebraic formulations derives from the fact that two quantum fields are physically equivalent when they generate the same algebras of local observables. Such equivalent quantum field theories belong to the same so-called Borchers class which entails that they lead to the same S

-matrix. As Haag (1996) stresses, fields are only an instrument in order to “coordinatize” observables, more precisely: sets of observables, with respect to different finite space-time regions. The choice of a particular field system is to a certain degree conventional, namely as long as it belongs to the same Borchers class. Thus it is more appropriate to consider these algebras, rather than quantum fields, as the fundamental entities in QFT. The resulting operationalistic view of QFT is that it is a statistical theory about local measurement outcomes, expressed in terms of local algebras of observables. Thus, it is no surprise that Haag’s (1996) famous textbook on “Algebraic QFT”, the most successful axiomatic reformulation, bears the title “Local Quantum Physics.”

​

not 1 letter