Off-shell Invariant D=N=2 Twisted Super Yang-Mills Theory with a Gauged Central Charge without Constraints

We formulate N=2 twisted super Yang-Mills theory with a gauged central charge by superconnection formalism in two dimensions. We obtain off-shell invariant supermultiplets and actions with and without constraints, which is in contrast with the off-shell invariant D=N=4 super Yang-Mills formulation with unavoidable constraints.Comment: 14 page

<ORGINAL ARTICLE>Evaluation of the Relationship between a Face Anxiety Scale and the State-Trait Anxiety Inventory

我々は簡単に短時間で患者の不安の程度を把握するために,我々が考案した顔不安スケール(Face Anxirty Scale FAS)を臨床で使用している。今回の研究はこのFASが不安をアセスメントする心理テスト,すなわちState-traitanxiety inventry (STAI)の得点に相関するのか検討した。FASとSTAIは歯科診療(口腔外科処置)前に待合室で実施し,患者自身に記入させた。尚,対象から対人恐怖症および自律神経失調症の患者は除外した。その結果,対象は33名(女性14名,男性19名),平均年齢は24.4才(19才から49才)。対象患者の多くは智歯の抜歯手術だった。歯科に関する既往歴は永久歯の抜歯経験が無い患者から歯科診療恐怖症の患者,精神鎮静法下に難抜歯の経験有る患者など,いろいろであった。今回は対象患者の約半数に対して,静脈内鎮静法(フルニトラゼパム投与)を施行した。特性不安はFASが0から2点,0.80±0 53(mean±S.D)であった。STAKA-trait)は32から64,43.46±8.29(mean±S.D.)となった。FASとSTAI(A-trait)の相関関係はFig2に示したように,Y=41.38+2.98X,R^2=0.04であった。歯科診療前の状態不安はFASが0から4点,平均1.94±1.35(mean±S.D )であった。STAI(A-state)は23から72,47.46±13.92(maen±S.D.)となった。FASとSTAI(A-trait)の相関関係はFig3に示したように,Y=30.22+8.87X,R^2=0.69(P <0.01)であった。以上の結果から,FASとSTAIの状態不安尺度は相関を認めた。従って,FASは歯科患者の状態不安を客観的,簡便に評価する事が認められた。また,我々が考案したFASは歯科治療に対する患者の不安評価方法として,有用性が示唆された。To determine the degree of fear of dental treatment in general, we applied a Face Anxiety Scale (FAS) for pre-operative levels of anxiousness. The FAS is valuable as it is easy and fast. The FAS assess anxiety at 6 levels, the lowest is 0, the highest 5. We assessed the pre-operative (minor dental surgery) anxiety of patients subject to intravenous sedeation, without psychosedation. To establish the reliability of the FAS, an evaluation of the relationship between the FAS and the State-trait anxiety inventory (STAI) was made. The pre-operative FAS ranged from 4 to 0 Anxiety with STAI (A-state) had a highest score of 72, and a lowest score of 23 The relationship between FAS and anxiety state with STAI was Y=30.22+8.87X,R^2=0.69(P<0 01). The FAS was significant correlated with state anxiety of STAI. The results suggest that FAS is a reliable measure for state anxiety in dental treatment

Twisted N=2 exact SUSY on the lattice for BF and Wess-Zumino

We formulate exact supersymmetric models on a lattice. We introduce noncommutativity to ensure the Leibniz rule. With the help of superspace formalism, we give supertransformations which keep the N=2 twisted SUSY algebra exactly. The action is given as a product of (anti)chiral superfields on the lattice. We present BF and Wess-Zumino models as explicit examples of our formulation. Both models have exact N=2 twisted SUSY in 2 dimensional space at a finite lattice spacing. In component fields, the action has supercharge exact form.Comment: 3 pages, 2 figures, talk presented by I. Kanamori at Lattice2004(Theory), Fermilab, 21-26 June 200

Twisted Superspace for N=D=2 Super BF and Yang-Mills with Dirac-K\"ahler Fermion Mechanism

We propose a twisted D=N=2 superspace formalism. The relation between the twisted super charges including the BRST charge, vector and pseudo scalar super charges and the N=2 spinor super charges is established. We claim that this relation is essentially related with the Dirac-K\"ahler fermion mechanism. We show that a fermionic bilinear form of twisted N=2 chiral and anti-chiral superfields is equivalent to the quantized version of BF theory with the Landau type gauge fixing while a bosonic bilinear form leads to the N=2 Wess-Zumino action. We then construct a Yang-Mills action described by the twisted N=2 chiral and vector superfields, and show that the action is equivalent to the twisted version of the D=N=2 super Yang-Mills action, previously obtained from the quantized generalized topological Yang-Mills action with instanton gauge fixing.Comment: 36 page

Formulation of Supersymmetry on a Lattice as a Representation of a Deformed Superalgebra

The lattice superalgebra of the link approach is shown to satisfy a Hopf algebraic supersymmetry where the difference operator is introduced as a momentum operator. The breakdown of the Leibniz rule for the lattice difference operator is accommodated as a coproduct operation of (quasi)triangular Hopf algebra and the associated field theory is consistently defined as a braided quantum field theory. Algebraic formulation of path integral is perturbatively defined and Ward-Takahashi identity can be derived on the lattice. The claimed inconsistency of the link approach leading to the ordering ambiguity for a product of fields is solved by introducing an almost trivial braiding structure corresponding to the triangular structure of the Hopf algebraic superalgebra. This could be seen as a generalization of spin and statistics relation on the lattice. From the consistency of this braiding structure of fields a grading nature for the momentum operator is required.Comment: 45 page

Riemann Integral of Functions from R into Real Normed Space

In this article, we define the Riemann integral on functions from R into real normed space and prove the linearity of this operator. As a result, the Riemann integration can be applied to a wider range of functions. The proof method follows the [16].Miyajima Keiichi - Faculty of Engineering, Ibaraki University, Hitachi, JapanKato Takahiro - Faculty of Engineering, Graduate School of Ibaraki University, Hitachi, JapanShidama Yasunari - Shinshu University, Nagano, JapanGrzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.Czesław Byliński. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990.Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.Noboru Endou and Artur Korniłowicz. The definition of the Riemann definite integral and some related lemmas. Formalized Mathematics, 8(1):93-102, 1999.Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Darboux's theorem. Formalized Mathematics, 9(1):197-200, 2001.Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Definition of integrability for partial functions from R to R and integrability for continuous functions. Formalized Mathematics, 9(2):281-284, 2001.Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Scalar multiple of Riemann definite integral. Formalized Mathematics, 9(1):191-196, 2001.Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990.Jarosław Kotowicz. Convergent sequences and the limit of sequences. Formalized Mathematics, 1(2):273-275, 1990.Beata Padlewska and Agata Darmochwał. Topological spaces and continuous functions. Formalized Mathematics, 1(1):223-230, 1990.Jan Popiołek. Real normed space. Formalized Mathematics, 2(1):111-115, 1991.Konrad Raczkowski and Paweł Sadowski. Topological properties of subsets in real numbers. Formalized Mathematics, 1(4):777-780, 1990.Murray R. Spiegel. Theory and Problems of Vector Analysis. McGraw-Hill, 1974.Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990.Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.Hiroshi Yamazaki and Yasunari Shidama. Algebra of vector functions. Formalized Mathematics, 3(2):171-175, 1992